MinT - Best Known (32−25, 32, s)-Nets in Base 256

Best Known (32−25, 32, s)-Nets in Base 256

(32−25, 32, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 32, 264)-net over F₂₅₆, using

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

(32−25, 32, 321)-Net over F₂₅₆ — Digital

Digital (7, 32, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 32, 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]

(32−25, 32, 34517)-Net in Base 256 — Upper bound on s

There is no (7, 32, 34518)-net in base 256, because

1 times m-reduction [i] would yield (7, 31, 34518)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 452 407811 941263 244160 363916 989830 116486 398515 636006 729317 390183 648459 219106 > 256³¹ [i]