Best Known (63−56, 63, s)-Nets in Base 9
(63−56, 63, 36)-Net over F9 — Constructive and digital
Digital (7, 63, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
(63−56, 63, 40)-Net over F9 — Digital
Digital (7, 63, 40)-net over F9, using
- net from sequence [i] based on digital (7, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 40, using
(63−56, 63, 76)-Net in Base 9 — Upper bound on s
There is no (7, 63, 77)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(963, 77, S9, 56), but
- the linear programming bound shows that M ≥ 8689 730220 804757 564506 468407 102842 427893 906077 785168 705860 479153 028329 / 5730 855145 > 963 [i]