MinT - Best Known (7, 7+53, s)-Nets in Base 256

Best Known (7, 7+53, s)-Nets in Base 256

(7, 7+53, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 60, 264)-net over F₂₅₆, using

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

(7, 7+53, 321)-Net over F₂₅₆ — Digital

Digital (7, 60, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 60, 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+53, 12054)-Net in Base 256 — Upper bound on s

There is no (7, 60, 12055)-net in base 256, because

1 times m-reduction [i] would yield (7, 59, 12055)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 12205 871245 240610 430085 834780 566216 412448 838110 921497 931715 345096 032681 361122 751113 060351 509463 313291 731647 227359 961185 277694 298479 517036 327776 > 256⁵⁹ [i]