Best Known (47−39, 47, s)-Nets in Base 16
(47−39, 47, 65)-Net over F16 — Constructive and digital
Digital (8, 47, 65)-net over F16, using
- t-expansion [i] based on digital (6, 47, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(47−39, 47, 424)-Net in Base 16 — Upper bound on s
There is no (8, 47, 425)-net in base 16, because
- 1 times m-reduction [i] would yield (8, 46, 425)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 24 878063 225793 176517 100670 127767 567405 716071 378541 467376 > 1646 [i]