Best Known (8, 149, s)-Nets in Base 9
(8, 149, 40)-Net over F9 — Constructive and digital
Digital (8, 149, 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
(8, 149, 42)-Net over F9 — Digital
Digital (8, 149, 42)-net over F9, using
- net from sequence [i] based on digital (8, 41)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 42, using
(8, 149, 81)-Net in Base 9 — Upper bound on s
There is no (8, 149, 82)-net in base 9, because
- 77 times m-reduction [i] would yield (8, 72, 82)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(972, 82, S9, 64), but
- the linear programming bound shows that M ≥ 81 263653 342333 764706 263468 532084 739047 417804 545994 203521 123805 237703 536792 532419 / 153444 711875 > 972 [i]
- extracting embedded orthogonal array [i] would yield OA(972, 82, S9, 64), but