Best Known (12, 12+37, s)-Nets in Base 81
(12, 12+37, 172)-Net over F81 — Constructive and digital
Digital (12, 49, 172)-net over F81, using
- t-expansion [i] based on digital (7, 49, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(12, 12+37, 298)-Net over F81 — Digital
Digital (12, 49, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
(12, 12+37, 11587)-Net in Base 81 — Upper bound on s
There is no (12, 49, 11588)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 48, 11588)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 40 486879 549339 739233 483885 854488 057726 828271 929202 010315 983798 039294 301931 406004 102815 393921 > 8148 [i]