MinT - Best Known (7, 7+57, s)-Nets in Base 256

Best Known (7, 7+57, s)-Nets in Base 256

(7, 7+57, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 64, 264)-net over F₂₅₆, using

net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(7, 7+57, 321)-Net over F₂₅₆ — Digital

Digital (7, 64, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 64, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(7, 7+57, 11601)-Net in Base 256 — Upper bound on s

There is no (7, 64, 11602)-net in base 256, because

1 times m-reduction [i] would yield (7, 63, 11602)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 52 499789 796238 245302 795605 550261 882756 611741 982989 702455 003132 815056 039787 752373 133849 184248 513003 315753 462938 093302 871837 239783 200022 853112 869084 430256 > 256⁶³ [i]