Best Known (3, 3+25, s)-Nets in Base 64
(3, 3+25, 104)-Net over F64 — Constructive and digital
Digital (3, 28, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
(3, 3+25, 113)-Net over F64 — Digital
Digital (3, 28, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
(3, 3+25, 966)-Net in Base 64 — Upper bound on s
There is no (3, 28, 967)-net in base 64, because
- 1 times m-reduction [i] would yield (3, 27, 967)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 5 853382 849268 715740 267375 771410 313335 205042 614120 > 6427 [i]