MinT - Best Known (27−20, 27, s)-Nets in Base 256

Best Known (27−20, 27, s)-Nets in Base 256

(27−20, 27, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 27, 264)-net over F₂₅₆, using

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

(27−20, 27, 321)-Net over F₂₅₆ — Digital

Digital (7, 27, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 27, 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]

(27−20, 27, 56448)-Net in Base 256 — Upper bound on s

There is no (7, 27, 56449)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 105329 617479 317013 252297 467633 839898 398937 095736 201519 830926 160576 > 256²⁷ [i]