MinT - Best Known (32, 32+44, s)-Nets in Base 32

Best Known (32, 32+44, s)-Nets in Base 32

(32, 32+44, 162)-Net over F₃₂ — Constructive and digital

Digital (32, 76, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 25, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (7, 51, 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]

(32, 32+44, 273)-Net over F₃₂ — Digital

Digital (32, 76, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 76, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(32, 32+44, 288)-Net in Base 32 — Constructive

(32, 76, 288)-net in base 32, using

t-expansion [i] based on (31, 76, 288)-net in base 32, using
- 1 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
  - base change [i] based on digital (9, 55, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(32, 32+44, 321)-Net in Base 32

(32, 76, 321)-net in base 32, using

4 times m-reduction [i] based on (32, 80, 321)-net in base 32, using
- base change [i] based on digital (2, 50, 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]

(32, 32+44, 46237)-Net in Base 32 — Upper bound on s

There is no (32, 76, 46238)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 463119 568102 552743 829638 560849 309411 028642 151185 001013 194045 119608 778547 765482 733138 181702 103579 438469 090456 457452 > 32⁷⁶ [i]