Best Known (9, 9+37, s)-Nets in Base 128
(9, 9+37, 288)-Net over F128 — Constructive and digital
Digital (9, 46, 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
(9, 9+37, 321)-Net in Base 128
(9, 46, 321)-net in base 128, using
- 10 times m-reduction [i] based on (9, 56, 321)-net in base 128, using
- base change [i] based on digital (2, 49, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 49, 321)-net over F256, using
(9, 9+37, 11015)-Net in Base 128 — Upper bound on s
There is no (9, 46, 11016)-net in base 128, because
- 1 times m-reduction [i] would yield (9, 45, 11016)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 66786 047983 126803 176254 356127 204143 659984 805006 986190 528035 369482 822384 126520 515443 892738 824400 > 12845 [i]