MinT - Best Known (31, 31+79, s)-Nets in Base 32

Best Known (31, 31+79, s)-Nets in Base 32

(31, 31+79, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(31, 31+79, 177)-Net in Base 32 — Constructive

(31, 110, 177)-net in base 32, using

32² times duplication [i] based on (29, 108, 177)-net in base 32, using
- t-expansion [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]

(31, 31+79, 273)-Net over F₃₂ — Digital

Digital (31, 110, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 110, 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]

(31, 31+79, 7973)-Net in Base 32 — Upper bound on s

There is no (31, 110, 7974)-net in base 32, because

1 times m-reduction [i] would yield (31, 109, 7974)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 304446 035122 872609 393032 383258 618274 996336 837205 261158 153097 019681 696098 095403 846906 656406 166813 375141 987555 060513 164189 270039 012589 851323 885802 509775 953538 646400 > 32¹⁰⁹ [i]