Best Known (122, s)-Sequences in Base 16
(122, 255)-Sequence over F16 — Constructive and digital
Digital (122, 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
(122, 257)-Sequence in Base 16 — Constructive
(122, 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
(122, 512)-Sequence over F16 — Digital
Digital (122, 512)-sequence over F16, using
- t-expansion [i] based on digital (118, 512)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 118 and N(F) ≥ 513, using
(122, 1875)-Sequence in Base 16 — Upper bound on s
There is no (122, 1876)-sequence in base 16, because
- net from sequence [i] would yield (122, m, 1877)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (122, 5627, 1877)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165627, 1877, S16, 3, 5505), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 128977 658309 571719 108198 919537 953899 821059 925539 207727 343992 615467 758732 878965 306707 979690 115376 185779 838897 361891 625825 289607 916313 954884 206745 289411 052191 892811 756018 720543 782414 786042 945257 442240 232184 393220 448680 700848 702028 289304 708916 485705 482738 454126 440525 210170 583732 478613 441566 174274 172820 574475 329700 138223 346317 942276 509308 647743 756970 680974 718446 093645 903220 287450 181900 623643 002520 922615 566717 731904 488358 298136 588869 421143 283166 846633 994263 040593 171287 600734 169130 358956 270441 313028 362477 692601 730775 285889 453440 037145 717914 212707 282595 183188 513021 907208 773804 441197 456184 160754 371218 745923 771025 344035 694722 189741 090110 403162 373136 309171 792084 407008 524243 495879 665737 343549 554582 404127 189933 110170 623282 981050 554126 797602 648716 280364 520135 992562 962240 971195 106997 745653 240144 403966 505115 819360 946826 203099 442421 526871 368829 524621 289164 435510 944533 006804 359616 926468 426302 387776 071093 719086 998524 085625 416047 492217 156508 617295 000873 574320 975407 169080 485629 004160 908886 479696 175066 135447 381355 745707 177656 962161 240942 480923 688171 185374 471241 382795 565817 333770 228469 844009 912319 599388 383366 465441 661968 746390 203547 479336 520906 006311 542370 228006 623924 113335 943349 536600 199734 146334 354719 918549 759962 819639 370392 534543 747933 121530 748336 694617 108167 337748 807621 852694 345244 802096 563051 817860 053822 323726 937515 619769 257184 365115 101096 936625 786270 443873 332340 782448 332730 122199 767753 010179 903961 506035 666163 431186 921133 783337 836605 913771 919261 143640 278221 927438 685231 502116 676895 536115 612425 212898 359490 840621 111048 546060 198764 771478 861470 764731 461914 761495 342784 480881 730343 414156 706492 878837 898294 531174 428095 747968 876515 329578 702553 736517 338652 226266 136390 166936 975261 019557 251312 942424 234688 770950 111783 121502 519121 563546 536007 423423 283637 742165 063816 782288 837265 959097 017875 117809 856168 719136 244959 487624 963320 862199 266624 368248 791363 128801 218854 481490 982028 863078 699615 069101 576043 439441 752882 681305 849438 949881 717506 467098 910497 391161 418169 483024 513812 364201 139064 053081 035015 451704 595800 879382 204091 044417 918229 702627 097245 299815 397703 252270 098887 837033 213453 845344 846416 736793 694169 356382 474901 478858 595374 296061 171981 356929 246159 344690 753115 619182 171621 887637 764207 018020 321347 904572 168504 199297 395102 300757 645169 276135 362411 380506 828217 680179 517534 501504 932723 236919 007905 257841 780157 220478 134146 766448 421622 295143 778992 345851 030962 751975 740476 024534 015178 129548 659983 975085 321986 995962 795055 114087 799683 674743 523349 966018 271728 731639 501756 256262 651960 642875 840315 936023 072584 393760 067200 062204 060283 810394 104120 089691 119052 792525 224008 807426 491089 873233 895603 480001 995885 545973 375728 612242 692360 409636 167757 622359 724474 496635 285717 868593 099476 819241 263478 290493 176734 455631 006601 617141 203033 826482 329591 680602 802775 093329 819179 078022 319660 092105 357579 559934 980419 398989 045027 128737 193652 166155 459385 929960 800208 202455 927920 975951 907972 296125 623225 336076 845748 538962 610644 171382 525006 644939 395865 266617 415225 188451 558113 447541 168558 943613 099789 681398 389254 334857 670922 339327 453425 399735 619882 896103 956078 871419 979002 251361 296908 737522 358373 276403 345838 371878 645338 485561 674183 254738 518180 750844 102536 664314 096738 896507 531209 186429 246946 144604 499818 044256 122721 769309 169083 221721 042361 920451 445477 627543 110072 891255 426669 843592 821580 182518 729432 716031 637567 187044 765611 031517 514692 409796 513791 776506 288866 562823 664108 227744 217221 444438 016543 396561 550272 197623 818403 020006 829825 227769 943403 956162 322184 886462 507050 272184 124842 247873 477468 451076 339521 666069 364923 185338 219223 422494 534877 507835 200047 002284 640713 018860 750972 599195 637533 985437 071623 628975 025506 591922 520769 471308 324826 171167 726080 879041 728487 441489 284244 996338 440531 026148 182058 725398 641389 032123 019408 899306 362309 321986 011198 921175 198649 168780 296487 787472 971131 371631 033742 832954 978940 931223 433423 830482 387316 824151 897543 617940 356270 773444 766054 226957 587435 892426 483315 890347 177649 033536 541975 771800 726382 932492 415444 653484 443897 709839 548625 529083 420698 742027 411743 264187 957100 930588 542282 163352 650869 099541 201234 321420 986666 555194 747184 105863 749671 144355 468274 821056 517247 036728 983237 658916 063002 851841 201814 215039 020645 118313 360989 753589 019105 053204 520885 845856 101966 025026 072320 394901 773139 421584 482784 047291 169155 787292 886263 900512 017159 064958 097740 908828 858509 392718 210581 043538 803870 669786 901697 516153 547297 240663 797598 025832 989016 463296 753450 326183 462249 971815 557354 592170 468025 138771 497762 933627 435111 266951 551206 571249 645477 815334 403792 284217 542894 723448 371500 482174 881282 625081 255875 548826 573648 820327 869266 864990 256750 438175 612101 295615 082282 889750 766069 882711 630715 442582 728741 100275 602316 372609 143047 158040 795535 501946 370484 999399 996030 669563 853484 890017 876431 040106 106344 940009 703515 534982 058896 293084 417540 090447 421963 401190 319685 670502 546099 659571 803036 675912 483286 958114 877594 387340 348019 790271 688577 264190 732690 495185 710312 917512 125545 547237 220061 259903 299129 762551 055244 229109 617710 044120 778339 670443 341357 454057 491501 736379 897456 403004 981572 486872 079088 139394 412410 891307 813075 700215 806590 733124 347219 538354 672211 005671 148671 499538 093029 749188 164026 305629 356125 589841 696767 542808 270983 586705 570077 781151 858892 338114 214700 465552 523487 208099 482644 546347 891521 546092 352076 062364 245297 361842 308234 269106 260460 604260 771636 789803 466609 346198 608156 064999 508638 536768 202184 765494 500593 107934 247278 228979 467136 833470 720573 039227 217739 873445 168642 960857 056527 182455 288535 649915 605955 206136 721625 558159 472114 313433 374245 006402 475251 813459 155398 174307 259916 531696 899158 676253 176215 350369 668310 698695 701114 241809 915453 327363 045272 559986 033367 907500 175817 158860 982712 891777 338825 901097 658148 323079 728080 000861 914613 743608 354218 031082 624184 305369 958590 055494 596969 157256 651099 941908 692212 453914 533969 819352 868993 065660 030939 547783 237340 694271 766751 086441 872405 933317 812849 083109 835536 087584 470028 330949 317801 552927 075731 413218 081631 171733 415050 618232 144334 644809 408118 637317 145867 398300 895646 954544 349825 779323 399000 270714 342870 969992 801566 926097 234603 553949 726095 899186 785411 780320 477954 353521 980941 853866 446206 291776 274962 224505 360446 260155 817503 317142 924619 982731 717086 048659 675784 016966 939041 363308 234932 481579 235858 201572 206877 365484 842281 412465 048966 885649 205404 421216 739819 577655 755868 957895 171462 388383 682423 302002 943256 998507 748126 214132 215819 909440 401831 786204 561739 935698 306860 678873 877585 003962 919133 859892 320466 900120 912925 737390 341557 220829 143656 216077 286085 805535 456195 359572 925462 986567 757721 981788 924322 865209 674749 343091 992105 990819 625533 318771 961402 117565 390114 268876 196310 198345 478897 025102 156541 368357 273498 740416 153632 461348 165248 202949 221584 009642 323489 776083 322684 505387 441221 336674 190969 372956 484183 820464 963613 440111 759446 367220 553970 806582 241837 478335 564427 511863 485013 141103 003938 050028 435664 905235 148424 907321 352267 973676 871667 774370 962371 895480 644294 178093 662208 / 2753 > 165627 [i]
- extracting embedded OOA [i] would yield OOA(165627, 1877, S16, 3, 5505), but
- m-reduction [i] would yield (122, 5627, 1877)-net in base 16, but