MinT - Best Known (14, 14+53, s)-Nets in Base 256

Best Known (14, 14+53, s)-Nets in Base 256

(14, 14+53, 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
- Niederreiter sequence [i]

(14, 14+53, 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
  - 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+53, 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 256^mÂ â‰¥ 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]