Best Known (61−54, 61, s)-Nets in Base 16
(61−54, 61, 65)-Net over F16 — Constructive and digital
Digital (7, 61, 65)-net over F16, using
- t-expansion [i] based on digital (6, 61, 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
(61−54, 61, 361)-Net in Base 16 — Upper bound on s
There is no (7, 61, 362)-net in base 16, because
- 8 times m-reduction [i] would yield (7, 53, 362)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 6684 408024 466728 093536 660646 380472 079625 367637 738874 536220 735416 > 1653 [i]