MinT - Best Known (7, 7+41, s)-Nets in Base 256

Best Known (7, 7+41, s)-Nets in Base 256

(7, 7+41, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 48, 264)-net over F₂₅₆, using

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

(7, 7+41, 321)-Net over F₂₅₆ — Digital

Digital (7, 48, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 48, 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+41, 14854)-Net in Base 256 — Upper bound on s

There is no (7, 48, 14855)-net in base 256, because

1 times m-reduction [i] would yield (7, 47, 14855)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 154074 315146 161580 175039 116093 321915 285478 517443 389477 344306 570244 951711 537924 467436 029369 064222 277268 907583 897376 > 256⁴⁷ [i]