Best Known (51−27, 51, s)-Nets in Base 16
(51−27, 51, 114)-Net over F16 — Constructive and digital
Digital (24, 51, 114)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- digital (6, 33, 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 (5, 18, 49)-net over F16, using
(51−27, 51, 164)-Net over F16 — Digital
Digital (24, 51, 164)-net over F16, using
(51−27, 51, 177)-Net in Base 16 — Constructive
(24, 51, 177)-net in base 16, using
- base change [i] based on digital (7, 34, 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
(51−27, 51, 16157)-Net in Base 16 — Upper bound on s
There is no (24, 51, 16158)-net in base 16, because
- 1 times m-reduction [i] would yield (24, 50, 16158)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 608212 480289 442067 735573 313056 594880 959290 475963 097529 963861 > 1650 [i]