Best Known (58−35, 58, s)-Nets in Base 3
(58−35, 58, 32)-Net over F3 — Constructive and digital
Digital (23, 58, 32)-net over F3, using
- t-expansion [i] based on digital (21, 58, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(58−35, 58, 122)-Net in Base 3 — Upper bound on s
There is no (23, 58, 123)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(358, 123, S3, 35), but
- the linear programming bound shows that M ≥ 201495 402622 906096 175334 816457 211875 092620 058002 548238 001408 261724 916634 589201 579113 225775 779369 702130 825086 476804 523253 066620 132151 818004 947363 262743 616021 484040 623486 572193 861459 098340 001855 700160 964173 244578 875000 735885 306199 742912 / 41 327530 790514 459377 762110 271277 431587 061903 941781 926336 577667 471683 540283 621826 442842 621380 985233 298612 494289 855885 360739 509599 463926 349730 935962 010030 346687 984858 018853 206876 419295 677262 929871 355942 656617 > 358 [i]