Best Known (38−33, 38, s)-Nets in Base 64
(38−33, 38, 128)-Net over F64 — Constructive and digital
Digital (5, 38, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
(38−33, 38, 133)-Net over F64 — Digital
Digital (5, 38, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
(38−33, 38, 1614)-Net in Base 64 — Upper bound on s
There is no (5, 38, 1615)-net in base 64, because
- 1 times m-reduction [i] would yield (5, 37, 1615)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 6 805169 497074 186079 472964 051774 345609 369148 404929 240317 827292 357060 > 6437 [i]