Best Known (77−42, 77, s)-Nets in Base 16
(77−42, 77, 130)-Net over F16 — Constructive and digital
Digital (35, 77, 130)-net over F16, using
- 4 times m-reduction [i] based on digital (35, 81, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 29, 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, 52, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 29, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(77−42, 77, 177)-Net in Base 16 — Constructive
(35, 77, 177)-net in base 16, using
- 7 times m-reduction [i] based on (35, 84, 177)-net in base 16, using
- base change [i] based on digital (7, 56, 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, 56, 177)-net over F64, using
(77−42, 77, 193)-Net over F16 — Digital
Digital (35, 77, 193)-net over F16, using
- t-expansion [i] based on digital (33, 77, 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
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
(77−42, 77, 209)-Net in Base 16
(35, 77, 209)-net in base 16, using
- 1 times m-reduction [i] based on (35, 78, 209)-net in base 16, using
- base change [i] based on digital (9, 52, 209)-net over F64, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 9 and N(F) ≥ 209, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- base change [i] based on digital (9, 52, 209)-net over F64, using
(77−42, 77, 15037)-Net in Base 16 — Upper bound on s
There is no (35, 77, 15038)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 521 763969 049259 781172 277158 045165 843108 634535 788314 761477 768176 491541 997013 930883 374574 961721 > 1677 [i]