MinT - Best Known (46−37, 46, s)-Nets in Base 256

Best Known (46−37, 46, s)-Nets in Base 256

(46−37, 46, 266)-Net over F₂₅₆ — Constructive and digital

Digital (9, 46, 266)-net over F₂₅₆, using

net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(46−37, 46, 513)-Net over F₂₅₆ — Digital

Digital (9, 46, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 46, 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]

(46−37, 46, 31050)-Net in Base 256 — Upper bound on s

There is no (9, 46, 31051)-net in base 256, because

1 times m-reduction [i] would yield (9, 45, 31051)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 349092 736005 959769 274249 022396 602007 400371 684301 657474 621143 672606 973832 299763 783295 624299 667610 522907 264916 > 256⁴⁵ [i]