MinT - Best Known (22, 50, s)-Nets in Base 32

Best Known (22, 50, s)-Nets in Base 32

(22, 50, 142)-Net over F₃₂ — Constructive and digital

Digital (22, 50, 142)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 15, 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, 35, 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]

(22, 50, 223)-Net over F₃₂ — Digital

Digital (22, 50, 223)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(22, 50, 259)-Net in Base 32 — Constructive

(22, 50, 259)-net in base 32, using

32² times duplication [i] based on (20, 48, 259)-net in base 32, using
- base change [i] based on digital (2, 30, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(22, 50, 321)-Net in Base 32

(22, 50, 321)-net in base 32, using

32² times duplication [i] based on (20, 48, 321)-net in base 32, using
- base change [i] based on digital (2, 30, 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]

(22, 50, 46298)-Net in Base 32 — Upper bound on s

There is no (22, 50, 46299)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1809 550554 161132 107517 293532 332550 104935 262133 962503 197962 495127 663607 922292 > 32⁵⁰ [i]