Best Known (45−39, 45, s)-Nets in Base 16
(45−39, 45, 65)-Net over F16 — Constructive and digital
Digital (6, 45, 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
(45−39, 45, 314)-Net in Base 16 — Upper bound on s
There is no (6, 45, 315)-net in base 16, because
- 1 times m-reduction [i] would yield (6, 44, 315)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 97969 310319 412772 705307 389093 982421 224219 103415 426776 > 1644 [i]