MinT - Best Known (42−36, 42, s)-Nets in Base 256

Best Known (42−36, 42, s)-Nets in Base 256

(42−36, 42, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 42, 263)-net over F₂₅₆, using

net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(42−36, 42, 321)-Net over F₂₅₆ — Digital

Digital (6, 42, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 42, 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]

(42−36, 42, 12317)-Net in Base 256 — Upper bound on s

There is no (6, 42, 12318)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 140133 610288 627035 037888 368991 485981 740818 173462 331377 871667 922745 907831 822073 617880 266425 395694 059946 > 256⁴² [i]