Best Known (31−27, 31, s)-Nets in Base 16
(31−27, 31, 45)-Net over F16 — Constructive and digital
Digital (4, 31, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
(31−27, 31, 220)-Net in Base 16 — Upper bound on s
There is no (4, 31, 221)-net in base 16, because
- 1 times m-reduction [i] would yield (4, 30, 221)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 391241 215915 656824 299197 858296 344896 > 1630 [i]