Best Known (51−41, 51, s)-Nets in Base 27
(51−41, 51, 94)-Net over F27 — Constructive and digital
Digital (10, 51, 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
(51−41, 51, 99)-Net over F27 — Digital
Digital (10, 51, 99)-net over F27, using
- t-expansion [i] based on digital (9, 51, 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
(51−41, 51, 1199)-Net in Base 27 — Upper bound on s
There is no (10, 51, 1200)-net in base 27, because
- 1 times m-reduction [i] would yield (10, 50, 1200)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 372253 538318 472901 419727 101411 688472 285119 790909 147340 318169 484848 760961 > 2750 [i]