MinT - Best Known (12, 12+32, s)-Nets in Base 256

Best Known (12, 12+32, s)-Nets in Base 256

(12, 12+32, 269)-Net over F₂₅₆ — Constructive and digital

Digital (12, 44, 269)-net over F₂₅₆, using

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

(12, 12+32, 513)-Net over F₂₅₆ — Digital

Digital (12, 44, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 44, 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+32, 111848)-Net in Base 256 — Upper bound on s

There is no (12, 44, 111849)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 9175 015408 733396 550918 634900 077155 080128 585197 682164 687631 076688 950032 461656 564242 091174 304825 670842 772046 > 256⁴⁴ [i]