Best Known (67−53, 67, s)-Nets in Base 256
(67−53, 67, 271)-Net over F256 — Constructive and digital
Digital (14, 67, 271)-net over F256, using
- net from sequence [i] based on digital (14, 270)-sequence over F256, using
(67−53, 67, 513)-Net over F256 — Digital
Digital (14, 67, 513)-net over F256, using
- t-expansion [i] based on digital (8, 67, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
(67−53, 67, 53687)-Net in Base 256 — Upper bound on s
There is no (14, 67, 53688)-net in base 256, because
- 1 times m-reduction [i] would yield (14, 66, 53688)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 878 786856 643896 340582 287142 889961 205074 661897 271665 946335 566366 919595 449943 245128 171155 716420 538686 318922 570630 564429 848018 970016 733441 627029 784904 804772 003316 > 25666 [i]