MinT - Best Known (33−26, 33, s)-Nets in Base 256

Best Known (33−26, 33, s)-Nets in Base 256

(33−26, 33, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 33, 264)-net over F₂₅₆, using

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

(33−26, 33, 321)-Net over F₂₅₆ — Digital

Digital (7, 33, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 33, 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]

(33−26, 33, 28840)-Net in Base 256 — Upper bound on s

There is no (7, 33, 28841)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 29 652442 086366 641054 048591 518756 520009 523149 520634 062396 058234 007756 031217 587616 > 256³³ [i]