MinT - Best Known (59−53, 59, s)-Nets in Base 256

Best Known (59−53, 59, s)-Nets in Base 256

(59−53, 59, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 59, 263)-net over F₂₅₆, using

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

(59−53, 59, 321)-Net over F₂₅₆ — Digital

Digital (6, 59, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 59, 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]

(59−53, 59, 9736)-Net in Base 256 — Upper bound on s

There is no (6, 59, 9737)-net in base 256, because

1 times m-reduction [i] would yield (6, 58, 9737)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 47 652006 651501 681955 460246 097847 483460 475816 838349 836717 466203 216371 078804 877931 276083 181437 377391 788287 783692 350917 814129 840701 518811 911936 > 256⁵⁸ [i]