MinT - Best Known (18, 18+41, s)-Nets in Base 256

Best Known (18, 18+41, s)-Nets in Base 256

(18, 18+41, 275)-Net over F₂₅₆ — Constructive and digital

Digital (18, 59, 275)-net over F₂₅₆, using

net from sequence [i] based on digital (18, 274)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(18, 18+41, 513)-Net over F₂₅₆ — Digital

Digital (18, 59, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 59, 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]

(18, 18+41, 313796)-Net in Base 256 — Upper bound on s

There is no (18, 59, 313797)-net in base 256, because

1 times m-reduction [i] would yield (18, 58, 313797)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 47 634308 211364 533255 472016 445880 871337 324455 842116 270419 848899 872595 038903 880311 935197 226763 285492 744847 314091 492783 467229 830956 801294 677076 > 256⁵⁸ [i]