Best Known (56−45, 56, s)-Nets in Base 9
(56−45, 56, 40)-Net over F9 — Constructive and digital
Digital (11, 56, 40)-net over F9, using
- t-expansion [i] based on digital (8, 56, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(56−45, 56, 55)-Net over F9 — Digital
Digital (11, 56, 55)-net over F9, using
- net from sequence [i] based on digital (11, 54)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 11 and N(F) ≥ 55, using
(56−45, 56, 252)-Net in Base 9 — Upper bound on s
There is no (11, 56, 253)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(956, 253, S9, 45), but
- the linear programming bound shows that M ≥ 14050 413158 089014 667096 845569 204561 136544 466572 675888 540662 732528 409097 562901 059332 582479 625210 442531 532800 / 49643 820062 566366 640194 027971 128601 762587 331729 491111 > 956 [i]