MinT - Best Known (27−25, 27, s)-Nets in Base 32

Best Known (27−25, 27, s)-Nets in Base 32

(27−25, 27, 44)-Net over F₃₂ — Constructive and digital

Digital (2, 27, 44)-net over F₃₂, using

t-expansion [i] based on digital (1, 27, 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]

(27−25, 27, 53)-Net over F₃₂ — Digital

Digital (2, 27, 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]

(27−25, 27, 291)-Net in Base 32 — Upper bound on s

There is no (2, 27, 292)-net in base 32, because

7 times m-reduction [i] would yield (2, 20, 292)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 281586 882188 718818 821592 427900 > 32²⁰ [i]