Best Known (10, 10+56, s)-Nets in Base 27
(10, 10+56, 94)-Net over F27 — Constructive and digital
Digital (10, 66, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
(10, 10+56, 99)-Net over F27 — Digital
Digital (10, 66, 99)-net over F27, using
- t-expansion [i] based on digital (9, 66, 99)-net over F27, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
(10, 10+56, 1013)-Net in Base 27 — Upper bound on s
There is no (10, 66, 1014)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 30005 139862 300099 885923 897153 975333 036417 763391 791188 386304 842155 044090 644758 447964 829276 872441 > 2766 [i]