MinT - Best Known (24, 24+28, s)-Nets in Base 32

Best Known (24, 24+28, s)-Nets in Base 32

(24, 24+28, 162)-Net over F₃₂ — Constructive and digital

Digital (24, 52, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 17, 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, 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]

(24, 24+28, 260)-Net in Base 32 — Constructive

(24, 52, 260)-net in base 32, using

4 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, 24+28, 293)-Net over F₃₂ — Digital

Digital (24, 52, 293)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 24+28, 321)-Net in Base 32

(24, 52, 321)-net in base 32, using

t-expansion [i] based on (23, 52, 321)-net in base 32, using
- 4 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, 24+28, 75964)-Net in Base 32 — Upper bound on s

There is no (24, 52, 75965)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 852683 831252 918567 292258 352573 779081 845732 176050 566059 376229 314952 413302 851848 > 32⁵² [i]