MinT - Best Known (52−50, 52, s)-Nets in Base 256

Best Known (52−50, 52, s)-Nets in Base 256

(52−50, 52, 259)-Net over F₂₅₆ — Constructive and digital

Digital (2, 52, 259)-net over F₂₅₆, using

net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(52−50, 52, 321)-Net over F₂₅₆ — Digital

Digital (2, 52, 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]

(52−50, 52, 3412)-Net in Base 256 — Upper bound on s

There is no (2, 52, 3413)-net in base 256, because

24 times m-reduction [i] would yield (2, 28, 3413)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 27 009154 831357 567488 514382 603415 649444 435571 933622 889000 358562 845296 > 256²⁸ [i]