Best Known (3, 3+28, s)-Nets in Base 81
(3, 3+28, 116)-Net over F81 — Constructive and digital
Digital (3, 31, 116)-net over F81, using
- t-expansion [i] based on digital (2, 31, 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
(3, 3+28, 136)-Net over F81 — Digital
Digital (3, 31, 136)-net over F81, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
(3, 3+28, 1264)-Net in Base 81 — Upper bound on s
There is no (3, 31, 1265)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 145909 130878 269199 657954 174239 182969 816972 052934 143523 944801 > 8131 [i]