Best Known (10, 10+37, s)-Nets in Base 27
(10, 10+37, 94)-Net over F27 — Constructive and digital
Digital (10, 47, 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+37, 99)-Net over F27 — Digital
Digital (10, 47, 99)-net over F27, using
- t-expansion [i] based on digital (9, 47, 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+37, 1312)-Net in Base 27 — Upper bound on s
There is no (10, 47, 1313)-net in base 27, because
- 1 times m-reduction [i] would yield (10, 46, 1313)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 702093 777397 806469 828923 641432 734069 028989 275939 883246 929829 774809 > 2746 [i]