MinT - Best Known (24, 24+32, s)-Nets in Base 32

Best Known (24, 24+32, s)-Nets in Base 32

(24, 24+32, 142)-Net over F₃₂ — Constructive and digital

Digital (24, 56, 142)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 17, 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]
2. digital (7, 39, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(24, 24+32, 225)-Net over F₃₂ — Digital

Digital (24, 56, 225)-net over F₃₂, using

net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(24, 24+32, 260)-Net in Base 32 — Constructive

(24, 56, 260)-net in base 32, using

base change [i] based on digital (3, 35, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(24, 24+32, 321)-Net in Base 32

(24, 56, 321)-net in base 32, using

t-expansion [i] based on (23, 56, 321)-net in base 32, using
- base change [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]

(24, 24+32, 40655)-Net in Base 32 — Upper bound on s

There is no (24, 56, 40656)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 943263 750247 458238 928479 927073 486598 327863 181489 249256 341852 845970 376412 297752 877580 > 32⁵⁶ [i]