Best Known (77−40, 77, s)-Nets in Base 128
(77−40, 77, 504)-Net over F128 — Constructive and digital
Digital (37, 77, 504)-net over F128, using
- t-expansion [i] based on digital (35, 77, 504)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 26, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (9, 51, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (5, 26, 216)-net over F128, using
- (u, u+v)-construction [i] based on
(77−40, 77, 549)-Net in Base 128 — Constructive
(37, 77, 549)-net in base 128, using
- (u, u+v)-construction [i] based on
- (8, 28, 261)-net in base 128, using
- 4 times m-reduction [i] based on (8, 32, 261)-net in base 128, using
- base change [i] based on digital (4, 28, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- base change [i] based on digital (4, 28, 261)-net over F256, using
- 4 times m-reduction [i] based on (8, 32, 261)-net in base 128, using
- digital (9, 49, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- (8, 28, 261)-net in base 128, using
(77−40, 77, 1773)-Net over F128 — Digital
Digital (37, 77, 1773)-net over F128, using
(77−40, 77, large)-Net in Base 128 — Upper bound on s
There is no (37, 77, large)-net in base 128, because
- 38 times m-reduction [i] would yield (37, 39, large)-net in base 128, but