MinT - Best Known (24, 54, s)-Nets in Base 32

Best Known (24, 54, s)-Nets in Base 32

(24, 54, 142)-Net over F₃₂ — Constructive and digital

Digital (24, 54, 142)-net over F₃₂, using

2 times m-reduction [i] based on digital (24, 56, 142)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 17, 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, 39, 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]

(24, 54, 246)-Net over F₃₂ — Digital

Digital (24, 54, 246)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 54, 260)-Net in Base 32 — Constructive

(24, 54, 260)-net in base 32, using

2 times m-reduction [i] based on (24, 56, 260)-net in base 32, using
- base change [i] based on digital (3, 35, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(24, 54, 321)-Net in Base 32

(24, 54, 321)-net in base 32, using

t-expansion [i] based on (23, 54, 321)-net in base 32, using
- 2 times m-reduction [i] based on (23, 56, 321)-net in base 32, using
  - base change [i] based on digital (2, 35, 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]

(24, 54, 54310)-Net in Base 32 — Upper bound on s

There is no (24, 54, 54311)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1897 319019 547716 224183 136790 629958 859508 848350 068100 893132 471443 908197 628248 686688 > 32⁵⁴ [i]