MinT - Best Known (108−73, 108, s)-Nets in Base 32

Best Known (108−73, 108, s)-Nets in Base 32

(108−73, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (35, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(108−73, 108, 192)-Net in Base 32 — Constructive

(35, 108, 192)-net in base 32, using

t-expansion [i] based on (34, 108, 192)-net in base 32, using
- base change [i] based on (16, 90, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
    - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(108−73, 108, 273)-Net over F₃₂ — Digital

Digital (35, 108, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 108, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(108−73, 108, 13690)-Net in Base 32 — Upper bound on s

There is no (35, 108, 13691)-net in base 32, because

1 times m-reduction [i] would yield (35, 107, 13691)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112574 935586 820973 166339 052458 374084 795470 584716 399117 723673 933588 224142 237373 450166 528454 483511 071151 108530 670425 812735 681189 587983 347160 688080 330984 857826 269342 > 32¹⁰⁷ [i]