Best Known (57−43, 57, s)-Nets in Base 128
(57−43, 57, 288)-Net over F128 — Constructive and digital
Digital (14, 57, 288)-net over F128, using
- t-expansion [i] based on digital (9, 57, 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
(57−43, 57, 353)-Net over F128 — Digital
Digital (14, 57, 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
(57−43, 57, 28428)-Net in Base 128 — Upper bound on s
There is no (14, 57, 28429)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 56, 28429)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 10087 598228 942480 162805 141120 605263 786623 906059 167822 436982 027780 398133 705959 813127 281593 694523 180397 092916 167269 628544 > 12856 [i]