MinT - Best Known (12, 12+43, s)-Nets in Base 256

Best Known (12, 12+43, s)-Nets in Base 256

(12, 12+43, 269)-Net over F₂₅₆ — Constructive and digital

Digital (12, 55, 269)-net over F₂₅₆, using

net from sequence [i] based on digital (12, 268)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(12, 12+43, 513)-Net over F₂₅₆ — Digital

Digital (12, 55, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 55, 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]

(12, 12+43, 53025)-Net in Base 256 — Upper bound on s

There is no (12, 55, 53026)-net in base 256, because

1 times m-reduction [i] would yield (12, 54, 53026)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 11091 747582 040080 791789 256810 351017 468687 668657 609748 927424 507432 820742 121500 607203 455800 599609 414961 550673 788630 653423 842093 928856 > 256⁵⁴ [i]