Best Known (12, 12+30, s)-Nets in Base 81
(12, 12+30, 172)-Net over F81 — Constructive and digital
Digital (12, 42, 172)-net over F81, using
- t-expansion [i] based on digital (7, 42, 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+30, 298)-Net over F81 — Digital
Digital (12, 42, 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+30, 17711)-Net in Base 81 — Upper bound on s
There is no (12, 42, 17712)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 143 386092 256928 181929 547037 698561 148034 917512 760231 777526 672036 238049 580962 310401 > 8142 [i]