Best Known (23, 48, s)-Nets in Base 16
(23, 48, 114)-Net over F16 — Constructive and digital
Digital (23, 48, 114)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 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, 31, 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, 17, 49)-net over F16, using
(23, 48, 172)-Net over F16 — Digital
Digital (23, 48, 172)-net over F16, using
(23, 48, 177)-Net in Base 16 — Constructive
(23, 48, 177)-net in base 16, using
- base change [i] based on digital (7, 32, 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
(23, 48, 18334)-Net in Base 16 — Upper bound on s
There is no (23, 48, 18335)-net in base 16, because
- 1 times m-reduction [i] would yield (23, 47, 18335)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 392 572029 612566 465433 453402 262943 091290 107231 008251 095801 > 1647 [i]