Best Known (58−43, 58, s)-Nets in Base 128
(58−43, 58, 288)-Net over F128 — Constructive and digital
Digital (15, 58, 288)-net over F128, using
- t-expansion [i] based on digital (9, 58, 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
(58−43, 58, 386)-Net over F128 — Digital
Digital (15, 58, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
(58−43, 58, 35820)-Net in Base 128 — Upper bound on s
There is no (15, 58, 35821)-net in base 128, because
- 1 times m-reduction [i] would yield (15, 57, 35821)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 1 291259 955364 195550 835172 713394 404116 782381 632950 797252 554648 903609 503972 727242 468079 528211 191082 236742 179849 618669 453008 > 12857 [i]