Best Known (63−32, 63, s)-Nets in Base 16
(63−32, 63, 257)-Net over F16 — Constructive and digital
Digital (31, 63, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(31,256) in PG(62,16)) for nets [i] based on digital (0, 32, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(63−32, 63, 24975)-Net in Base 16 — Upper bound on s
There is no (31, 63, 24976)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 7237 515063 440020 587122 804355 062367 973070 165212 498879 832985 891004 042933 470616 > 1663 [i]