Best Known (67−54, 67, s)-Nets in Base 128
(67−54, 67, 288)-Net over F128 — Constructive and digital
Digital (13, 67, 288)-net over F128, using
- t-expansion [i] based on digital (9, 67, 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
(67−54, 67, 321)-Net over F128 — Digital
Digital (13, 67, 321)-net over F128, using
- t-expansion [i] based on digital (12, 67, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(67−54, 67, 14561)-Net in Base 128 — Upper bound on s
There is no (13, 67, 14562)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1525 169455 127916 569129 938510 164842 222224 607170 959516 336275 176100 370733 904806 397629 305468 579544 503086 288632 554562 954250 891863 532631 061604 172592 > 12867 [i]