MinT - Best Known (7, 7+47, s)-Nets in Base 256

Best Known (7, 7+47, s)-Nets in Base 256

(7, 7+47, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 54, 264)-net over F₂₅₆, using

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

(7, 7+47, 321)-Net over F₂₅₆ — Digital

Digital (7, 54, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 54, 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+47, 13090)-Net in Base 256 — Upper bound on s

There is no (7, 54, 13091)-net in base 256, because

1 times m-reduction [i] would yield (7, 53, 13091)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 43 327320 790118 005383 631680 378090 792682 696743 521588 326139 831758 149608 317499 789773 436400 786497 011969 957095 970845 738498 417107 648416 > 256⁵³ [i]