MinT - Best Known (1, 27, s)-Nets in Base 256

Best Known (1, 27, s)-Nets in Base 256

(1, 27, 258)-Net over F₂₅₆ — Constructive and digital

Digital (1, 27, 258)-net over F₂₅₆, using

net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(1, 27, 289)-Net over F₂₅₆ — Digital

Digital (1, 27, 289)-net over F₂₅₆, using

net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
  - sharp bound on the number of rational points on curves with genus 1 [i]

(1, 27, 1915)-Net in Base 256 — Upper bound on s

There is no (1, 27, 1916)-net in base 256, because

12 times m-reduction [i] would yield (1, 15, 1916)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 1 333267 576803 339800 949754 838517 444586 > 256¹⁵ [i]