MinT - Best Known (52−50, 52, s)-Nets in Base 32

Best Known (52−50, 52, s)-Nets in Base 32

(52−50, 52, 44)-Net over F₃₂ — Constructive and digital

Digital (2, 52, 44)-net over F₃₂, using

t-expansion [i] based on digital (1, 52, 44)-net over F₃₂, using
- net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
    - a function field by SÃ©mirat [i]

(52−50, 52, 53)-Net over F₃₂ — Digital

Digital (2, 52, 53)-net over F₃₂, using

net from sequence [i] based on digital (2, 52)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 2 and N(F) ≥ 53, using
  - sharp bound on the number of rational points on curves with genus 2 [i]

(52−50, 52, 249)-Net in Base 32 — Upper bound on s

There is no (2, 52, 250)-net in base 32, because

extracting embedded orthogonal array [i] would yield OA(32⁵², 250, S₃₂, 50), but
- the linear programming bound shows that MÂ â‰¥ 252 768740 691192 179837 675764 301770 844055 514644 392911 853329 538720 148817 830269 842909 641032 595406 848000 / 135 614536 236051 811447 > 32⁵² [i]