MinT - Best Known (7, 40, s)-Nets in Base 256

Best Known (7, 40, s)-Nets in Base 256

(7, 40, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 40, 264)-net over F₂₅₆, using

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

(7, 40, 321)-Net over F₂₅₆ — Digital

Digital (7, 40, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 40, 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, 40, 19765)-Net in Base 256 — Upper bound on s

There is no (7, 40, 19766)-net in base 256, because

1 times m-reduction [i] would yield (7, 39, 19766)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 8344 146436 068978 014035 777107 129043 525942 284862 217514 448218 620421 400238 231230 541656 287610 054531 > 256³⁹ [i]