Best Known (12−10, 12, s)-Nets in Base 81
(12−10, 12, 116)-Net over F81 — Constructive and digital
Digital (2, 12, 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
(12−10, 12, 118)-Net over F81 — Digital
Digital (2, 12, 118)-net over F81, using
- net from sequence [i] based on digital (2, 117)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 118, using
(12−10, 12, 1237)-Net in Base 81 — Upper bound on s
There is no (2, 12, 1238)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 80072 791747 378108 719201 > 8112 [i]