Best Known (8, 8+68, s)-Nets in Base 16
(8, 8+68, 65)-Net over F16 — Constructive and digital
Digital (8, 76, 65)-net over F16, using
- t-expansion [i] based on digital (6, 76, 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
(8, 8+68, 408)-Net in Base 16 — Upper bound on s
There is no (8, 76, 409)-net in base 16, because
- 16 times m-reduction [i] would yield (8, 60, 409)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 822339 856650 198012 911195 259157 124016 349729 875467 036119 357675 385495 075136 > 1660 [i]