Best Known (79−54, 79, s)-Nets in Base 16
(79−54, 79, 65)-Net over F16 — Constructive and digital
Digital (25, 79, 65)-net over F16, using
- t-expansion [i] based on digital (6, 79, 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
(79−54, 79, 104)-Net in Base 16 — Constructive
(25, 79, 104)-net in base 16, using
- 1 times m-reduction [i] based on (25, 80, 104)-net in base 16, using
- base change [i] based on digital (9, 64, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 64, 104)-net over F32, using
(79−54, 79, 144)-Net over F16 — Digital
Digital (25, 79, 144)-net over F16, using
- net from sequence [i] based on digital (25, 143)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 25 and N(F) ≥ 144, using
(79−54, 79, 2414)-Net in Base 16 — Upper bound on s
There is no (25, 79, 2415)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 134207 202169 779250 507967 862218 957950 107581 439760 082003 230618 249552 568827 418835 379497 414869 887576 > 1679 [i]