Best Known (31−30, 31, s)-Nets in Base 128
(31−30, 31, 150)-Net over F128 — Constructive and digital
Digital (1, 31, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
(31−30, 31, 864)-Net in Base 128 — Upper bound on s
There is no (1, 31, 865)-net in base 128, because
- 18 times m-reduction [i] would yield (1, 13, 865)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 2484 523883 258978 205576 739312 > 12813 [i]