Best Known (43−23, 43, s)-Nets in Base 128
(43−23, 43, 429)-Net over F128 — Constructive and digital
Digital (20, 43, 429)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (1, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (1, 24, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (0, 7, 129)-net over F128, using
(43−23, 43, 517)-Net in Base 128 — Constructive
(20, 43, 517)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 14, 258)-net in base 128, using
- 2 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- 2 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- (6, 29, 259)-net in base 128, using
- 3 times m-reduction [i] based on (6, 32, 259)-net in base 128, using
- base change [i] based on digital (2, 28, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 28, 259)-net over F256, using
- 3 times m-reduction [i] based on (6, 32, 259)-net in base 128, using
- (3, 14, 258)-net in base 128, using
(43−23, 43, 948)-Net over F128 — Digital
Digital (20, 43, 948)-net over F128, using
(43−23, 43, 4294580)-Net in Base 128 — Upper bound on s
There is no (20, 43, 4294581)-net in base 128, because
- 1 times m-reduction [i] would yield (20, 42, 4294581)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 31828 755116 903808 406351 756016 872590 262927 170761 783042 215936 266953 611472 572765 816330 017528 > 12842 [i]