Best Known (31−19, 31, s)-Nets in Base 81
(31−19, 31, 216)-Net over F81 — Constructive and digital
Digital (12, 31, 216)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (2, 21, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (1, 10, 100)-net over F81, using
(31−19, 31, 298)-Net over F81 — Digital
Digital (12, 31, 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
(31−19, 31, 119196)-Net in Base 81 — Upper bound on s
There is no (12, 31, 119197)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 30, 119197)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 1797 089170 669939 838894 352235 577547 723629 856999 587217 905041 > 8130 [i]