MinT - Best Known (28, 61, s)-Nets in Base 32

Best Known (28, 61, s)-Nets in Base 32

(28, 61, 174)-Net over F₃₂ — Constructive and digital

Digital (28, 61, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 21, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 40, 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]

(28, 61, 288)-Net in Base 32 — Constructive

(28, 61, 288)-net in base 32, using

5 times m-reduction [i] based on (28, 66, 288)-net in base 32, using
- base change [i] based on (17, 55, 288)-net in base 64, using
  - 1 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
    - base change [i] based on digital (9, 48, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(28, 61, 315)-Net over F₃₂ — Digital

Digital (28, 61, 315)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 61, 321)-Net in Base 32

(28, 61, 321)-net in base 32, using

t-expansion [i] based on (27, 61, 321)-net in base 32, using
- 5 times m-reduction [i] based on (27, 66, 321)-net in base 32, using
  - base change [i] based on (16, 55, 321)-net in base 64, using
    - 1 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
      - base change [i] based on digital (2, 42, 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]

(28, 61, 96706)-Net in Base 32 — Upper bound on s

There is no (28, 61, 96707)-net in base 32, because

1 times m-reduction [i] would yield (28, 60, 96707)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 037370 595869 296329 018767 362250 071134 741211 305870 357918 966454 186963 576828 758533 245539 515620 > 32⁶⁰ [i]