MinT - Best Known (35−29, 35, s)-Nets in Base 256

Best Known (35−29, 35, s)-Nets in Base 256

(35−29, 35, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 35, 263)-net over F₂₅₆, using

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

(35−29, 35, 321)-Net over F₂₅₆ — Digital

Digital (6, 35, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 35, 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]

(35−29, 35, 16723)-Net in Base 256 — Upper bound on s

There is no (6, 35, 16724)-net in base 256, because

1 times m-reduction [i] would yield (6, 34, 16724)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 7590 997106 089184 287621 044141 703636 970362 100788 451564 673016 932782 358582 631157 106556 > 256³⁴ [i]