MinT - Best Known (26, 26+75, s)-Nets in Base 32

Best Known (26, 26+75, s)-Nets in Base 32

(26, 26+75, 120)-Net over F₃₂ — Constructive and digital

Digital (26, 101, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 101, 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]

(26, 26+75, 177)-Net in Base 32 — Constructive

(26, 101, 177)-net in base 32, using

t-expansion [i] based on (25, 101, 177)-net in base 32, using
- 7 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
  - base change [i] based on digital (7, 90, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(26, 26+75, 225)-Net over F₃₂ — Digital

Digital (26, 101, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 101, 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+75, 5508)-Net in Base 32 — Upper bound on s

There is no (26, 101, 5509)-net in base 32, because

1 times m-reduction [i] would yield (26, 100, 5509)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 289910 363360 147288 008243 875209 531891 079943 695580 411359 105199 099751 383097 872187 423493 965973 269154 768056 414989 474027 876194 801244 520012 407134 466688 624384 > 32¹⁰⁰ [i]