MinT - Best Known (14, 14+41, s)-Nets in Base 256

Best Known (14, 14+41, s)-Nets in Base 256

(14, 14+41, 271)-Net over F₂₅₆ — Constructive and digital

Digital (14, 55, 271)-net over F₂₅₆, using

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

(14, 14+41, 513)-Net over F₂₅₆ — Digital

Digital (14, 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]

(14, 14+41, 103507)-Net in Base 256 — Upper bound on s

There is no (14, 55, 103508)-net in base 256, because

1 times m-reduction [i] would yield (14, 54, 103508)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 11090 753658 278833 145651 819132 839273 858765 475068 051969 156727 460026 302394 721149 851210 482752 690704 992216 244030 675189 126136 519264 396176 > 256⁵⁴ [i]