Best Known (80−68, 80, s)-Nets in Base 27
(80−68, 80, 96)-Net over F27 — Constructive and digital
Digital (12, 80, 96)-net over F27, using
- t-expansion [i] based on digital (11, 80, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(80−68, 80, 109)-Net over F27 — Digital
Digital (12, 80, 109)-net over F27, using
- net from sequence [i] based on digital (12, 108)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 12 and N(F) ≥ 109, using
(80−68, 80, 1196)-Net in Base 27 — Upper bound on s
There is no (12, 80, 1197)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 246995 434645 175137 229770 692049 521386 406376 144007 958323 718647 925868 653477 513452 182318 719725 439101 107016 510922 334897 > 2780 [i]