MinT - Best Known (36−29, 36, s)-Nets in Base 256

Best Known (36−29, 36, s)-Nets in Base 256

(36−29, 36, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 36, 264)-net over F₂₅₆, using

net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(36−29, 36, 321)-Net over F₂₅₆ — Digital

Digital (7, 36, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 36, 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]

(36−29, 36, 24854)-Net in Base 256 — Upper bound on s

There is no (7, 36, 24855)-net in base 256, because

1 times m-reduction [i] would yield (7, 35, 24855)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 1 943345 899730 502425 929403 229861 070424 073117 859813 694805 360403 949339 300840 155582 935226 > 256³⁵ [i]