Best Known (41−32, 41, s)-Nets in Base 128
(41−32, 41, 288)-Net over F128 — Constructive and digital
Digital (9, 41, 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
(41−32, 41, 321)-Net in Base 128
(9, 41, 321)-net in base 128, using
- 15 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
(41−32, 41, 13434)-Net in Base 128 — Upper bound on s
There is no (9, 41, 13435)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 248 877331 948550 299286 027065 892109 084114 858755 431022 568014 061051 813856 716336 205523 076741 > 12841 [i]