Best Known (58−30, 58, s)-Nets in Base 128
(58−30, 58, 480)-Net over F128 — Constructive and digital
Digital (28, 58, 480)-net over F128, using
- 2 times m-reduction [i] based on digital (28, 60, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 19, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (9, 41, 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 (3, 19, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(58−30, 58, 546)-Net in Base 128 — Constructive
(28, 58, 546)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 19, 258)-net in base 128, using
- 5 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
- 5 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- digital (9, 39, 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
- (4, 19, 258)-net in base 128, using
(58−30, 58, 1520)-Net over F128 — Digital
Digital (28, 58, 1520)-net over F128, using
(58−30, 58, 7109532)-Net in Base 128 — Upper bound on s
There is no (28, 58, 7109533)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 165 264221 262310 764945 695257 510084 549125 612257 039406 310010 231310 061247 808304 952284 956573 612333 629695 105733 575663 887293 355536 > 12858 [i]