Best Known (64−55, 64, s)-Nets in Base 128
(64−55, 64, 288)-Net over F128 — Constructive and digital
Digital (9, 64, 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
(64−55, 64, 289)-Net in Base 128
(9, 64, 289)-net in base 128, using
- base change [i] based on digital (1, 56, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
(64−55, 64, 7089)-Net in Base 128 — Upper bound on s
There is no (9, 64, 7090)-net in base 128, because
- 1 times m-reduction [i] would yield (9, 63, 7090)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 5 688397 496953 797853 181189 468656 565585 293043 514315 312194 427551 420108 394363 573044 862326 229948 617150 472379 432397 729422 104832 919638 760304 > 12863 [i]