Best Known (64−34, 64, s)-Nets in Base 16
(64−34, 64, 130)-Net over F16 — Constructive and digital
Digital (30, 64, 130)-net over F16, using
- 2 times m-reduction [i] based on digital (30, 66, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 24, 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
- digital (6, 42, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 24, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(64−34, 64, 177)-Net in Base 16 — Constructive
(30, 64, 177)-net in base 16, using
- 5 times m-reduction [i] based on (30, 69, 177)-net in base 16, using
- base change [i] based on digital (7, 46, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 46, 177)-net over F64, using
(64−34, 64, 187)-Net over F16 — Digital
Digital (30, 64, 187)-net over F16, using
(64−34, 64, 16321)-Net in Base 16 — Upper bound on s
There is no (30, 64, 16322)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 115813 665306 771574 006570 033260 822119 505856 154569 575726 620699 081987 394724 987036 > 1664 [i]