Best Known (40, 40+63, s)-Nets in Base 16
(40, 40+63, 225)-Net over F16 — Constructive and digital
Digital (40, 103, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
(40, 40+63, 7566)-Net in Base 16 — Upper bound on s
There is no (40, 103, 7567)-net in base 16, because
- 1 times m-reduction [i] would yield (40, 102, 7567)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 661 845424 802721 383440 036663 298477 406258 784910 181087 141102 370523 737555 307828 149220 501209 522239 040295 210585 796257 379571 430656 > 16102 [i]