Best Known (27, 27+32, s)-Nets in Base 128
(27, 27+32, 438)-Net over F128 — Constructive and digital
Digital (27, 59, 438)-net over F128, using
- 2 times m-reduction [i] based on digital (27, 61, 438)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 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 (9, 43, 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 (1, 18, 150)-net over F128, using
- (u, u+v)-construction [i] based on
(27, 27+32, 517)-Net in Base 128 — Constructive
(27, 59, 517)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 20, 258)-net in base 128, using
- 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- base change [i] based on digital (1, 21, 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, 21, 258)-net over F256, using
- 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- (7, 39, 259)-net in base 128, using
- 1 times m-reduction [i] based on (7, 40, 259)-net in base 128, using
- base change [i] based on digital (2, 35, 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, 35, 259)-net over F256, using
- 1 times m-reduction [i] based on (7, 40, 259)-net in base 128, using
- (4, 20, 258)-net in base 128, using
(27, 27+32, 1017)-Net over F128 — Digital
Digital (27, 59, 1017)-net over F128, using
(27, 27+32, 3155518)-Net in Base 128 — Upper bound on s
There is no (27, 59, 3155519)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 21153 855158 327590 057910 404720 431093 172200 439896 190202 564938 959424 237402 315481 074151 097568 873057 369700 765883 131814 672573 846405 > 12859 [i]