Best Known (129, s)-Sequences in Base 16
(129, 255)-Sequence over F16 — Constructive and digital
Digital (129, 255)-sequence over F16, using
- t-expansion [i] based on digital (75, 255)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
(129, 257)-Sequence in Base 16 — Constructive
(129, 257)-sequence in base 16, using
- t-expansion [i] based on (113, 257)-sequence in base 16, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
(129, 532)-Sequence over F16 — Digital
Digital (129, 532)-sequence over F16, using
- t-expansion [i] based on digital (123, 532)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 123 and N(F) ≥ 533, using
(129, 1980)-Sequence in Base 16 — Upper bound on s
There is no (129, 1981)-sequence in base 16, because
- net from sequence [i] would yield (129, m, 1982)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (129, 5942, 1982)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165942, 1982, S16, 3, 5813), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 279759 446578 491666 552270 376112 992660 659718 983491 219894 904410 815800 672873 824811 193188 075326 534511 696096 248615 999362 167538 414317 817298 176612 844547 334649 089639 329599 949302 922437 617882 394962 828727 132436 782664 846910 638331 149416 756473 621357 272774 968351 028610 610838 536211 923587 875682 380442 450387 983738 448513 806661 741192 992372 057191 290164 677595 248807 904525 920216 217865 830343 221391 425815 396541 574498 473122 502972 101164 712971 703700 270931 869375 577926 782305 405488 576258 743779 522312 049719 519575 022278 997311 164715 980026 569869 402914 752829 266332 713667 186992 028031 517167 546516 221360 288910 068832 677594 086360 048568 217642 606443 498320 186933 193232 638745 008598 122843 588926 072627 200743 981440 652916 720163 311805 627482 344630 937353 532731 323869 196926 047027 880006 724965 741842 461947 456603 755460 469246 460205 902395 099257 969721 131106 961251 230148 999414 920411 691595 011537 758512 781554 453490 934120 683137 748733 774515 070616 274797 429200 554200 027136 252040 643391 352977 416496 114628 251920 529326 686539 356134 590814 980344 145911 987692 738410 439179 154754 459590 431611 489526 088226 893233 892593 219097 975427 755180 372943 165589 670798 735445 787871 021491 493808 220035 938653 891865 421577 454779 612351 205501 382253 916612 254757 808448 298311 628776 040767 526905 082577 400403 275422 644365 163272 387828 186957 423588 992168 859915 339722 303396 487291 515472 039239 524805 781651 630461 288450 813411 658342 284741 947159 880284 665685 154424 124883 829407 758790 623283 101569 376145 673278 419893 027823 622163 181921 988484 524087 930522 815231 413925 731267 387360 949569 332839 390022 444364 769485 467900 946516 037846 426397 560402 439079 412046 071075 161668 306953 459361 597937 952839 209614 344187 049741 663720 301397 111958 095021 394691 396387 458375 913044 598111 233775 248359 761943 890840 606571 586495 730631 296470 141315 986082 247711 515839 512613 104929 555895 818731 635769 026172 675675 801821 435482 534050 141919 521442 931867 417172 212164 129797 217183 404879 111449 069715 324024 831935 238666 625659 228177 674222 000794 837286 738498 762937 322362 088856 315984 725842 037022 167142 192099 026289 718751 793472 432264 218881 458175 586576 867198 781412 303511 880612 424897 878721 446001 338976 861099 522624 794487 865404 494130 324934 390231 124490 894805 540479 312519 658043 375769 191044 424681 012915 548333 996232 037631 314269 628355 605530 563779 157599 511492 455623 112437 575370 085586 033454 518963 974981 083875 822478 806050 320264 687951 576908 334248 084624 286234 723035 604550 314692 750439 404882 847199 028710 421234 566643 220077 966233 977436 545687 835528 918428 343124 750510 883756 256612 360320 389932 697562 698431 867359 243299 440809 951164 601033 084180 496330 048946 523738 486914 942444 222450 080604 187103 608570 043439 902887 803066 122926 417126 150116 108580 229412 607467 429351 056793 842219 549153 469971 912565 715521 117416 797009 248629 323827 222604 995998 679789 421911 601041 869983 836600 864229 342329 724172 709272 522644 634950 132160 734031 061365 055357 248229 191785 022695 571319 320086 612500 814074 026036 100891 947028 336380 296877 673354 726562 934680 075616 314647 348370 519097 145708 614855 365845 895525 441432 538526 888483 427757 906358 554006 053366 844506 853499 364500 294512 992661 789702 203035 777235 128267 162086 047340 758683 314343 698071 562827 300215 051156 434863 176931 220802 146037 342192 587004 506252 315725 185702 036135 635792 151221 012486 115778 424749 844821 134219 171523 664184 143825 518458 045823 995268 647475 583672 579798 722500 714765 497188 281310 610083 922007 508628 925154 833241 955826 500540 985051 967423 133751 632346 830546 716653 838940 726496 131625 703922 758752 561201 435734 710870 777726 925408 700611 508389 650332 625862 235115 718954 897674 922344 357836 635963 127912 274420 199215 207492 129674 282370 689647 839464 270820 098121 974142 837689 999517 458758 163203 576205 196634 937360 520426 846797 133340 102412 343995 904097 957250 139509 662796 160032 011954 389017 254070 920412 014004 156162 186611 486760 806422 912669 578359 695059 967990 053830 240666 040977 890198 794899 615302 282981 666110 664495 898512 296157 786068 006206 244951 873491 736940 961942 297593 966501 810917 725247 753583 278980 238974 088327 060240 292844 591403 593870 140119 686503 525412 694556 403077 755784 947142 734550 905665 009079 087853 340025 503174 678410 854455 960197 914325 166022 977684 354569 153953 914031 775796 880019 494463 526960 315969 685009 030107 625628 385924 421068 559832 455639 292474 448012 396062 603672 245565 860025 285938 710668 881218 897671 934555 922081 036562 723823 150961 520399 311173 492069 580238 836771 468237 394743 928680 527341 649665 840022 275863 521109 271495 382127 052960 492562 674850 968710 324022 814274 904400 300209 984740 429893 596072 371473 693125 003785 647037 566462 651342 627897 117531 301633 753762 918965 584248 119543 738337 885674 988322 570691 580246 837000 624962 906919 839061 718950 486342 385683 595661 201605 277659 988981 531914 549243 701543 141992 072395 252902 957237 949423 263001 998772 238790 748209 898859 337227 877437 188605 590423 576843 778066 430478 617804 716047 962693 833009 160565 189856 424183 808423 694050 692002 338150 608632 693212 937974 900626 459560 075651 130108 448069 231408 822808 544055 222637 408974 249382 128768 306287 849265 396215 926443 518017 591057 610589 754897 424671 979232 196530 889812 218698 208638 326984 922696 692835 446604 108626 284978 565137 499703 600815 225200 941158 831832 487138 925951 258127 540860 868228 860691 339974 566117 856794 649232 135489 390483 191000 900089 832976 432575 616479 227999 767419 436208 409141 101610 098309 513828 975008 016011 576995 660562 684335 418940 591129 572310 859970 189778 599955 554622 023003 176660 351871 082495 141128 101861 374719 858665 082874 284233 470275 887311 262823 104213 881774 417881 984853 017022 979682 191503 068184 577733 558249 837612 112433 172418 939836 080552 435726 811500 806793 478938 273595 493469 882516 914566 846179 884471 129887 416763 135578 398942 827794 846647 745108 725672 694715 305594 350166 616587 414703 145206 189853 588719 768956 848942 178958 071071 495223 735949 908426 108687 134252 939904 950493 160329 663297 671264 079770 996271 960806 397322 524607 958184 170345 838047 799400 911689 838673 832376 742864 061057 087929 703924 978572 071760 013884 489195 011870 805835 959052 705925 803946 545026 076019 865989 519871 812876 217441 729117 417004 749686 572540 935051 859340 106734 351053 918617 147638 958494 098927 567400 377016 375095 545764 336528 915525 226189 310594 789922 677059 254047 964745 981406 723302 094400 693557 192905 437168 569039 981531 077915 194225 773147 867996 680157 706797 366000 752610 884655 062427 369410 716416 701851 058566 171624 560139 040282 712646 371896 418135 138508 064965 884976 166679 917942 783698 961212 956026 434984 938799 980285 498982 050503 616934 574862 503061 790593 296065 994304 483223 679952 005233 460341 831723 216562 298969 667801 895737 527129 738896 636401 119734 343640 860695 082309 634773 659997 311973 846370 563830 564037 666388 125990 983410 172920 360456 439367 241750 767068 851133 155097 019922 845460 109962 148067 850608 531170 682895 123550 500485 381063 211544 267289 683880 800386 483356 023990 316067 018897 063833 827355 625675 377696 431154 194709 834706 924018 786193 523530 307401 982257 633426 117564 058937 710990 438177 482289 700248 013297 906578 322072 759894 869238 482323 994042 961058 877911 587976 372069 580396 204075 351133 966360 087492 184690 826188 016105 928976 401706 505890 215957 017216 505579 842587 541572 836194 838972 948387 792833 825404 557201 796177 575977 178718 732276 418272 466140 426161 004404 550338 021402 082045 383131 386155 986133 194913 362508 012718 292382 770876 706478 600935 413845 886092 615676 937220 591384 523856 389937 764868 387188 599901 375839 376148 207996 522738 483953 001210 372623 883971 706893 141946 097063 540674 820397 348269 577997 287190 709313 260322 160329 087286 244539 799519 947893 613487 843122 094802 284255 648475 700577 364754 658777 510797 298883 259794 224431 252457 964567 863885 700971 152658 441589 723806 288911 011611 502085 931008 / 323 > 165942 [i]
- extracting embedded OOA [i] would yield OOA(165942, 1982, S16, 3, 5813), but
- m-reduction [i] would yield (129, 5942, 1982)-net in base 16, but