MinT - Best Known (39−29, 39, s)-Nets in Base 256

Best Known (39−29, 39, s)-Nets in Base 256

(39−29, 39, 267)-Net over F₂₅₆ — Constructive and digital

Digital (10, 39, 267)-net over F₂₅₆, using

net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(39−29, 39, 513)-Net over F₂₅₆ — Digital

Digital (10, 39, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 39, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(39−29, 39, 81570)-Net in Base 256 — Upper bound on s

There is no (10, 39, 81571)-net in base 256, because

1 times m-reduction [i] would yield (10, 38, 81571)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 32 594456 605032 785444 448086 268154 990324 907880 889589 029951 293130 236361 438266 017751 786449 469496 > 256³⁸ [i]