Best Known (74, 74+75, s)-Nets in Base 9
(74, 74+75, 165)-Net over F9 — Constructive and digital
Digital (74, 149, 165)-net over F9, using
- t-expansion [i] based on digital (64, 149, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(74, 74+75, 267)-Net over F9 — Digital
Digital (74, 149, 267)-net over F9, using
(74, 74+75, 11994)-Net in Base 9 — Upper bound on s
There is no (74, 149, 11995)-net in base 9, because
- 1 times m-reduction [i] would yield (74, 148, 11995)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1693 814612 003998 991493 828264 477143 977671 323508 524088 317344 760507 215715 190010 325544 671348 664148 484033 311377 257300 161661 934170 813767 782444 523065 > 9148 [i]