MinT - Best Known (30, 30+43, s)-Nets in Base 32

Best Known (30, 30+43, s)-Nets in Base 32

(30, 30+43, 142)-Net over F₃₂ — Constructive and digital

Digital (30, 73, 142)-net over F₃₂, using

1 times m-reduction [i] based on digital (30, 74, 142)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 23, 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, 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]

(30, 30+43, 259)-Net in Base 32 — Constructive

(30, 73, 259)-net in base 32, using

32¹ times duplication [i] based on (29, 72, 259)-net in base 32, using
- base change [i] based on digital (2, 45, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(30, 30+43, 273)-Net over F₃₂ — Digital

Digital (30, 73, 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]

(30, 30+43, 321)-Net in Base 32

(30, 73, 321)-net in base 32, using

32¹ times duplication [i] based on (29, 72, 321)-net in base 32, using
- base change [i] based on digital (2, 45, 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]

(30, 30+43, 40507)-Net in Base 32 — Upper bound on s

There is no (30, 73, 40508)-net in base 32, because

1 times m-reduction [i] would yield (30, 72, 40508)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 349697 740413 014992 344140 917971 008392 783504 185115 407390 307538 201275 054303 843647 545916 588325 700166 828795 984002 > 32⁷² [i]