Best Known (70−41, 70, s)-Nets in Base 3
(70−41, 70, 37)-Net over F3 — Constructive and digital
Digital (29, 70, 37)-net over F3, using
- t-expansion [i] based on digital (27, 70, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(70−41, 70, 42)-Net over F3 — Digital
Digital (29, 70, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(70−41, 70, 159)-Net in Base 3 — Upper bound on s
There is no (29, 70, 160)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(370, 160, S3, 41), but
- the linear programming bound shows that M ≥ 237 414600 825052 605339 898199 161036 160905 519527 864586 535472 314868 452096 658656 264978 116155 882452 002220 053256 435156 976668 686347 726403 430562 706599 352511 621348 216092 041159 803048 965786 298333 323258 611041 118871 189616 553496 629315 483774 972599 246302 034772 157493 244417 809960 760744 207521 818016 988413 507021 348142 213336 494925 / 92442 752096 604942 178479 892415 842808 407405 887791 675287 977155 119754 877305 147007 945880 487028 463385 092034 013239 252418 811114 453981 675714 908592 981461 034409 612784 987754 955522 814374 638703 922669 543339 745948 692352 108779 197259 513447 911227 390404 751701 831689 423908 878212 005188 779482 752082 > 370 [i]