MinT - Best Known (26, 26+34, s)-Nets in Base 32

Best Known (26, 26+34, s)-Nets in Base 32

(26, 26+34, 142)-Net over F₃₂ — Constructive and digital

Digital (26, 60, 142)-net over F₃₂, using

2 times m-reduction [i] based on digital (26, 62, 142)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 19, 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, 43, 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]

(26, 26+34, 233)-Net over F₃₂ — Digital

Digital (26, 60, 233)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+34, 260)-Net in Base 32 — Constructive

(26, 60, 260)-net in base 32, using

base change [i] based on (16, 50, 260)-net in base 64, using
- 2 times m-reduction [i] based on (16, 52, 260)-net in base 64, using
  - base change [i] based on digital (3, 39, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(26, 26+34, 321)-Net in Base 32

(26, 60, 321)-net in base 32, using

4 times m-reduction [i] based on (26, 64, 321)-net in base 32, using
- base change [i] based on digital (2, 40, 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]

(26, 26+34, 47511)-Net in Base 32 — Upper bound on s

There is no (26, 60, 47512)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 037345 901205 794730 339088 525194 691361 016200 018319 313844 665058 920499 999430 396222 998432 297429 > 32⁶⁰ [i]