Best Known (55−43, 55, s)-Nets in Base 128
(55−43, 55, 288)-Net over F128 — Constructive and digital
Digital (12, 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
(55−43, 55, 321)-Net over F128 — Digital
Digital (12, 55, 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
(55−43, 55, 17905)-Net in Base 128 — Upper bound on s
There is no (12, 55, 17906)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 54, 17906)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 616140 792856 617362 063647 178286 043898 269238 725732 186429 792656 284126 922104 989519 034976 983722 973883 286098 246643 073256 > 12854 [i]