Best Known (126, s)-Sequences in Base 16
(126, 255)-Sequence over F16 — Constructive and digital
Digital (126, 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
(126, 257)-Sequence in Base 16 — Constructive
(126, 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
(126, 532)-Sequence over F16 — Digital
Digital (126, 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
(126, 1935)-Sequence in Base 16 — Upper bound on s
There is no (126, 1936)-sequence in base 16, because
- net from sequence [i] would yield (126, m, 1937)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (126, 5807, 1937)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165807, 1937, S16, 3, 5681), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 234878 935627 850329 011384 820394 942815 643815 965970 128768 118620 327509 758254 728015 663472 215602 466731 216999 265142 805840 941916 247536 491889 667346 128678 976469 532483 259630 773891 781735 554107 685839 899646 154345 465901 361034 258327 023106 793052 987567 488417 759627 902071 944839 778439 626435 094355 360617 528394 418421 364786 667294 117235 135429 630995 854306 538456 611779 364338 443389 543323 182521 315215 352506 874946 588312 514107 618874 320173 413924 654076 786051 023249 844137 812216 602759 035953 794749 979904 056308 932007 269152 437081 945352 451993 558114 020476 405499 128064 055103 866035 376390 210080 917069 132433 580148 503489 359015 760816 550775 198569 840386 940808 454851 980786 413453 806470 341567 935882 967128 532424 662170 612990 914922 701331 740121 286607 269035 922312 214784 238853 528197 936783 342833 352281 318075 147908 100763 816463 984323 684975 683089 091993 021499 888267 976307 588559 958575 924367 257235 259089 317576 447072 425472 215870 758837 743706 536013 740307 978630 989752 853732 730198 929975 273973 703572 016418 576336 560567 992001 722900 904223 589847 398425 658093 116595 888699 616169 167868 242760 894217 652820 949845 053585 118922 435373 399650 153688 521225 898126 352956 732164 432859 592708 708504 823645 941896 347306 701711 296641 607914 247494 319713 011044 170159 334808 926442 854271 318492 495404 204335 016383 424032 264817 518082 506765 617040 195489 540305 193724 669364 096822 115804 440527 435973 479683 271207 441270 595830 351563 973294 959149 221458 835146 437613 075612 315858 396676 975697 564279 166823 998388 448334 578531 819982 596287 962172 693693 332418 595895 462762 020460 546855 125190 571832 946105 663913 152608 301153 967053 712583 615916 928848 936675 197016 116323 355238 993503 060345 907533 319297 115970 171055 869633 894239 304973 992200 762614 277081 536336 308070 938600 533657 733233 157362 399100 205939 437137 407644 803525 788890 956152 857083 572802 755959 236683 962445 387300 613252 386444 933243 975748 113634 070358 396275 702688 755299 858348 837540 239677 956092 995323 572396 475765 912519 102837 943330 879519 856010 793689 486756 381275 648349 513516 170581 912614 302378 731150 128964 518705 330178 830843 202675 325007 690961 283659 973172 424849 872043 064587 390666 318495 355163 410663 295595 840887 511207 455359 960928 049806 327935 838507 615484 504105 978491 448308 753663 756591 856517 508174 829865 633569 146345 370624 570498 807512 880957 720719 613006 890065 800953 634653 097468 810724 008821 219578 079542 851212 510649 415196 818939 956926 437768 412580 396453 226095 981593 718800 798355 052359 915236 319916 867202 916391 122672 182473 108076 910640 454298 764890 761794 296319 425933 097630 119004 163865 751540 394131 401190 271976 466497 026565 635206 759227 013903 807707 507150 490376 857257 904096 480400 766677 016603 346754 533568 908118 929609 827488 671942 445154 200676 763276 806130 012772 964214 561067 502299 702240 934816 708633 911551 526521 364071 620672 041667 678298 340317 331996 485461 778212 105996 063500 687380 853278 116686 403057 660946 504759 829637 669214 978097 281492 110435 155867 912300 821713 786556 358843 368279 016610 085479 501670 672627 899544 953791 280386 798895 204824 625835 703108 237028 527867 706616 282635 635504 399021 025623 400925 812733 180841 829809 055079 264703 767065 069925 508690 781628 787162 834921 512563 911831 798680 428332 028282 119490 787775 391814 688908 231107 915739 452909 266141 216915 572073 643108 013724 249902 477389 251420 954581 588198 614636 969251 193687 084221 203580 743260 295551 251349 671522 529217 773052 522169 825610 281953 821821 396269 395159 982916 375360 031323 148734 824014 003613 339114 402815 825063 099278 572429 603493 820175 566916 729601 667394 692220 875882 204421 253798 633930 826953 181680 239008 488840 780826 856017 027717 077105 543295 785726 183465 720956 234431 326309 582283 220249 684248 572803 671853 952851 319631 471895 191446 613115 813255 809475 485831 986334 297858 827422 282450 518238 847646 506440 298200 486195 767260 352241 419869 458886 181597 851322 151384 046182 191385 771943 091158 215884 085190 376467 565427 116229 319698 040775 836081 564752 551283 449295 026579 738923 298632 547092 376679 472680 115813 044595 387848 733769 941007 193912 626404 329127 525974 249193 717852 249785 983790 420175 314145 259696 280008 480621 106286 338537 438508 193248 961923 908298 960843 369301 847015 760171 426572 331962 814764 239346 944941 981864 903290 066028 986444 840766 472603 789399 202546 749402 070663 397589 597287 548663 750479 534843 672598 820231 187430 253421 026516 810835 192192 142968 088252 367930 866201 955885 592871 889374 768429 141815 080860 278764 759986 789103 372195 772084 990912 580736 481312 288107 995535 439360 997735 652284 510822 360194 758546 723982 883760 618964 082466 152962 567734 122250 230744 584575 581043 360037 998791 028991 522769 509047 324534 057247 883401 640585 455496 799717 045484 783188 868905 894671 104991 217833 416132 179510 485091 488012 044844 234187 124954 259875 220010 510626 480637 496699 060732 237480 206687 779049 575820 247345 072861 121453 597125 442240 674468 355058 928588 200726 804648 570293 160905 962369 422042 677123 491236 230835 294006 373886 565327 289013 550799 798460 453817 578813 640283 026165 891622 006120 822624 569718 312157 198700 509351 575639 511389 666952 733185 248725 504036 490633 594313 588870 390083 039925 723976 428205 283270 468552 065378 143119 901879 945431 759055 853783 973026 643618 316322 774290 799746 383279 703033 943605 094107 866522 520837 036091 287057 322445 551471 918195 310810 969525 631975 402089 265979 180689 705977 902886 004118 479008 892009 200875 496532 709116 154077 499842 512969 124845 965272 556123 035824 052085 460331 540081 595824 780292 555225 332627 735217 528394 526949 108410 376127 839936 744728 182289 222653 900850 450474 345891 122695 885341 139248 831146 595132 443718 568356 168540 926087 977402 851342 256080 461205 237069 595808 858146 762846 670311 610348 614436 788779 888932 897134 953350 780546 723823 791551 516334 360594 983290 981827 170022 586003 861157 083001 477980 986433 950931 228859 661080 410203 180600 159023 620279 171858 824375 569301 503735 828580 599911 921966 094584 290023 263725 995246 398209 697889 253393 736413 065437 562090 778285 891793 460078 210336 023597 156030 614665 708375 591787 936245 441960 468734 434402 985407 125004 361987 701386 354894 343732 348707 534259 089326 298469 253384 186083 456777 169288 980406 118394 126778 619819 479372 531926 491542 021834 766587 891210 517064 410845 302800 480734 136722 085619 504515 272988 007732 623473 066828 006418 325854 098862 733309 553847 878245 311805 422142 067527 897361 163947 979665 986604 429574 154466 796062 305112 697547 542589 528741 128676 497047 775257 064768 438922 516376 751825 028082 274725 974661 884595 064618 722864 848846 680540 479327 025382 958612 339607 175936 854740 304669 041991 645419 057204 405130 972469 529173 071091 923780 450106 167926 929038 063724 749349 556437 054780 540585 262899 504646 406193 335885 881518 350562 208612 852022 695229 835521 142084 549019 294240 558526 450246 563325 131224 391833 101173 534344 202480 548187 219999 340417 874609 927548 134937 969026 531308 997417 186254 131212 292588 904152 992189 746853 567610 233570 779177 315314 029806 489147 884937 464872 896002 454310 469310 952796 116149 260732 648079 456946 683377 921614 478905 430030 512991 825727 764877 881416 471744 807894 756399 387452 415180 746209 267733 255659 991478 520318 591194 837081 722077 449173 410590 356006 654418 410358 767492 947244 629663 975039 563535 598449 089352 513459 646929 500479 151690 456299 009799 127135 735966 474830 273165 061746 503092 014761 343194 169751 616000 545352 156134 321247 997096 430856 772778 466080 113336 628992 171360 879465 729491 868619 800139 315314 092007 339594 522762 629199 022593 102375 000882 469234 654005 677795 058700 532303 444577 170581 564967 355806 337246 958805 237442 395981 380721 657956 174278 058964 974364 853554 641986 239358 680244 331901 469777 519623 506515 532103 811072 / 947 > 165807 [i]
- extracting embedded OOA [i] would yield OOA(165807, 1937, S16, 3, 5681), but
- m-reduction [i] would yield (126, 5807, 1937)-net in base 16, but