MinT - Best Known (60−55, 60, s)-Nets in Base 256

Best Known (60−55, 60, s)-Nets in Base 256

(60−55, 60, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 60, 262)-net over F₂₅₆, using

net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(60−55, 60, 321)-Net over F₂₅₆ — Digital

Digital (5, 60, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 60, 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]

(60−55, 60, 7826)-Net in Base 256 — Upper bound on s

There is no (5, 60, 7827)-net in base 256, because

1 times m-reduction [i] would yield (5, 59, 7827)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 12197 984745 263951 605495 540408 652307 908096 628169 753609 456585 627220 736656 544549 996312 334186 646135 530571 592529 919252 199206 048320 408971 139222 132096 > 256⁵⁹ [i]