Best Known (24, 24+33, s)-Nets in Base 16
(24, 24+33, 98)-Net over F16 — Constructive and digital
Digital (24, 57, 98)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 18, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (6, 39, 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 (2, 18, 33)-net over F16, using
(24, 24+33, 128)-Net in Base 16 — Constructive
(24, 57, 128)-net in base 16, using
- base change [i] based on digital (5, 38, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(24, 24+33, 129)-Net over F16 — Digital
Digital (24, 57, 129)-net over F16, using
- t-expansion [i] based on digital (19, 57, 129)-net over F16, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 19 and N(F) ≥ 129, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
(24, 24+33, 133)-Net in Base 16
(24, 57, 133)-net in base 16, using
- base change [i] based on digital (5, 38, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
(24, 24+33, 7419)-Net in Base 16 — Upper bound on s
There is no (24, 57, 7420)-net in base 16, because
- 1 times m-reduction [i] would yield (24, 56, 7420)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 26 997188 761334 589783 570944 238327 374541 573656 409758 474063 812672 938301 > 1656 [i]