MinT - Best Known (7, 7+23, s)-Nets in Base 256

Best Known (7, 7+23, s)-Nets in Base 256

(7, 7+23, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 30, 264)-net over F₂₅₆, using

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

(7, 7+23, 321)-Net over F₂₅₆ — Digital

Digital (7, 30, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 30, 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+23, 42995)-Net in Base 256 — Upper bound on s

There is no (7, 30, 42996)-net in base 256, because

1 times m-reduction [i] would yield (7, 29, 42996)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 6903 274681 268356 132316 558323 691283 492138 952755 938077 864028 861525 451406 > 256²⁹ [i]