Best Known (61−32, 61, s)-Nets in Base 128
(61−32, 61, 480)-Net over F128 — Constructive and digital
Digital (29, 61, 480)-net over F128, using
- 2 times m-reduction [i] based on digital (29, 63, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 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, 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 (3, 20, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(61−32, 61, 546)-Net in Base 128 — Constructive
(29, 61, 546)-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
- 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
- (4, 20, 258)-net in base 128, using
(61−32, 61, 1385)-Net over F128 — Digital
Digital (29, 61, 1385)-net over F128, using
(61−32, 61, 5787252)-Net in Base 128 — Upper bound on s
There is no (29, 61, 5787253)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 346 584070 187412 193952 485481 615833 997545 556665 208552 151856 668063 454191 423520 820865 131289 709526 859211 774400 239856 423651 490457 417439 > 12861 [i]