MinT - Best Known (33, 33+47, s)-Nets in Base 32

Best Known (33, 33+47, s)-Nets in Base 32

(33, 33+47, 162)-Net over F₃₂ — Constructive and digital

Digital (33, 80, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 26, 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, 54, 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]

(33, 33+47, 273)-Net over F₃₂ — Digital

Digital (33, 80, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 80, 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]

(33, 33+47, 288)-Net in Base 32 — Constructive

(33, 80, 288)-net in base 32, using

4 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 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]

(33, 33+47, 321)-Net in Base 32

(33, 80, 321)-net in base 32, using

t-expansion [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]

(33, 33+47, 44961)-Net in Base 32 — Upper bound on s

There is no (33, 80, 44962)-net in base 32, because

1 times m-reduction [i] would yield (33, 79, 44962)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80701 558293 069168 045751 362536 796130 022114 831074 872140 664074 546923 732025 744450 379431 232335 185912 936553 551100 406531 181360 > 32⁷⁹ [i]