MinT - Best Known (26, 26+38, s)-Nets in Base 32

Best Known (26, 26+38, s)-Nets in Base 32

(26, 26+38, 131)-Net over F₃₂ — Constructive and digital

Digital (26, 64, 131)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 19, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
2. digital (7, 45, 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+38, 225)-Net over F₃₂ — Digital

Digital (26, 64, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 64, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(26, 26+38, 259)-Net in Base 32 — Constructive

(26, 64, 259)-net in base 32, using

base change [i] based on digital (2, 40, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(26, 26+38, 321)-Net in Base 32

(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+38, 30039)-Net in Base 32 — Upper bound on s

There is no (26, 64, 30040)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 136565 086126 307894 056731 448054 918087 601974 936522 910690 449893 704056 347294 785083 970601 261291 150533 > 32⁶⁴ [i]