MinT - Best Known (11−8, 11, s)-Nets in Base 256

Best Known (11−8, 11, s)-Nets in Base 256

(11−8, 11, 260)-Net over F₂₅₆ — Constructive and digital

Digital (3, 11, 260)-net over F₂₅₆, using

net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(11−8, 11, 321)-Net over F₂₅₆ — Digital

Digital (3, 11, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 11, 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]

(11−8, 11, 36404)-Net in Base 256 — Upper bound on s

There is no (3, 11, 36405)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 309 503771 048517 149436 164101 > 256¹¹ [i]