Best Known (90, s)-Sequences in Base 5
(90, 81)-Sequence over F5 — Constructive and digital
Digital (90, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
(90, 149)-Sequence over F5 — Digital
Digital (90, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
(90, 377)-Sequence in Base 5 — Upper bound on s
There is no (90, 378)-sequence in base 5, because
- net from sequence [i] would yield (90, m, 379)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (90, 1511, 379)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51511, 379, S5, 4, 1421), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1301 631837 001181 630131 341853 092428 183444 712028 509554 450845 457924 968233 883202 358910 568176 768950 557594 172676 758900 026412 157334 027068 660249 479226 951379 115547 551980 027813 538379 328093 890602 258448 953349 637476 172742 817759 481786 812632 776550 375980 604033 832944 118999 707541 342721 613871 871322 896612 718029 293148 003313 335608 523856 500104 854387 666021 341247 729647 252797 710766 307207 931444 173975 814706 227367 155021 117328 172599 714153 563300 631080 735569 226522 412259 810965 521110 610975 921803 101617 094292 005936 770400 071248 415631 118083 646269 971149 835385 718954 864222 173948 112739 385784 205357 343352 644046 347515 923183 327313 819281 617289 241022 288948 040369 860588 904747 722318 677053 284244 710163 547199 447834 106864 318483 757397 237411 970555 361788 105264 108975 174681 270197 169061 243274 583897 849146 558999 675114 159272 735415 065166 556090 388232 484366 793868 191023 103360 121584 802956 237903 580469 182869 618269 176282 956727 019296 998517 796018 150850 859696 053856 004532 091304 255277 494257 607498 223205 781450 582325 373627 418261 428860 286442 490077 170601 085715 934345 144783 182514 605017 303377 376691 742028 924636 542797 088623 046875 / 711 > 51511 [i]
- extracting embedded OOA [i] would yield OOA(51511, 379, S5, 4, 1421), but
- m-reduction [i] would yield (90, 1511, 379)-net in base 5, but