Best Known (56−47, 56, s)-Nets in Base 81
(56−47, 56, 172)-Net over F81 — Constructive and digital
Digital (9, 56, 172)-net over F81, using
- t-expansion [i] based on digital (7, 56, 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
(56−47, 56, 244)-Net over F81 — Digital
Digital (9, 56, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
(56−47, 56, 4305)-Net in Base 81 — Upper bound on s
There is no (9, 56, 4306)-net in base 81, because
- 1 times m-reduction [i] would yield (9, 55, 4306)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 929 852558 150558 579864 430042 511115 111528 077830 745967 217294 191390 143804 560430 865877 663455 800512 267193 478241 > 8155 [i]