MinT - Best Known (12−11, 12, s)-Nets in Base 256

Best Known (12−11, 12, s)-Nets in Base 256

(12−11, 12, 258)-Net over F₂₅₆ — Constructive and digital

Digital (1, 12, 258)-net over F₂₅₆, using

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

(12−11, 12, 289)-Net over F₂₅₆ — Digital

Digital (1, 12, 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]

(12−11, 12, 2027)-Net in Base 256 — Upper bound on s

There is no (1, 12, 2028)-net in base 256, because

1 times m-reduction [i] would yield (1, 11, 2028)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 309 756388 573549 153507 602826 > 256¹¹ [i]