Best Known (55−41, 55, s)-Nets in Base 128
(55−41, 55, 288)-Net over F128 — Constructive and digital
Digital (14, 55, 288)-net over F128, using
- t-expansion [i] based on digital (9, 55, 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
(55−41, 55, 353)-Net over F128 — Digital
Digital (14, 55, 353)-net over F128, using
- net from sequence [i] based on digital (14, 352)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 14 and N(F) ≥ 353, using
(55−41, 55, 31977)-Net in Base 128 — Upper bound on s
There is no (14, 55, 31978)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 54, 31978)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 616025 072263 785009 800918 246774 609994 463571 327521 814452 748245 054746 976467 409063 992183 210305 034553 029130 858403 795996 > 12854 [i]