Best Known (64−35, 64, s)-Nets in Base 128
(64−35, 64, 480)-Net over F128 — Constructive and digital
Digital (29, 64, 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, 44, 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
(64−35, 64, 545)-Net in Base 128 — Constructive
(29, 64, 545)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 20, 257)-net in base 128, using
- 4 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- 4 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (9, 44, 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
- (3, 20, 257)-net in base 128, using
(64−35, 64, 1004)-Net over F128 — Digital
Digital (29, 64, 1004)-net over F128, using
(64−35, 64, 3640933)-Net in Base 128 — Upper bound on s
There is no (29, 64, 3640934)-net in base 128, because
- 1 times m-reduction [i] would yield (29, 63, 3640934)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 5 678438 734295 887062 603499 011154 609691 241723 453387 171629 609258 870459 616432 855200 543580 824570 926812 269807 798338 761510 071962 101026 239902 > 12863 [i]