MinT - Best Known (14, 14+37, s)-Nets in Base 256

Best Known (14, 14+37, s)-Nets in Base 256

(14, 14+37, 271)-Net over F₂₅₆ — Constructive and digital

Digital (14, 51, 271)-net over F₂₅₆, using

net from sequence [i] based on digital (14, 270)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(14, 14+37, 513)-Net over F₂₅₆ — Digital

Digital (14, 51, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 51, 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]

(14, 14+37, 144917)-Net in Base 256 — Upper bound on s

There is no (14, 51, 144918)-net in base 256, because

1 times m-reduction [i] would yield (14, 50, 144918)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 582536 704377 719554 189425 838352 790577 373943 361853 344973 617135 758500 518670 096228 699209 983657 800608 770654 031422 217216 888946 > 256⁵⁰ [i]