Best Known (75−42, 75, s)-Nets in Base 16
(75−42, 75, 130)-Net over F16 — Constructive and digital
Digital (33, 75, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 27, 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, 48, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 27, 65)-net over F16, using
(75−42, 75, 177)-Net in Base 16 — Constructive
(33, 75, 177)-net in base 16, using
- 3 times m-reduction [i] based on (33, 78, 177)-net in base 16, using
- base change [i] based on digital (7, 52, 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, 52, 177)-net over F64, using
(75−42, 75, 193)-Net over F16 — Digital
Digital (33, 75, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
(75−42, 75, 11545)-Net in Base 16 — Upper bound on s
There is no (33, 75, 11546)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 040014 669394 662758 000525 872163 581058 701025 000169 925839 088195 912041 696714 680877 108297 437366 > 1675 [i]