MinT - Best Known (13, 86, s)-Nets in Base 32

Best Known (13, 86, s)-Nets in Base 32

(13, 86, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 86, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 86, 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]

(13, 86, 129)-Net over F₃₂ — Digital

Digital (13, 86, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 86, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(13, 86, 1630)-Net in Base 32 — Upper bound on s

There is no (13, 86, 1631)-net in base 32, because

1 times m-reduction [i] would yield (13, 85, 1631)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 87 956589 082423 232071 873036 369909 365850 229340 660419 246674 830011 654921 083912 351598 034068 414239 478823 865428 447834 234391 493041 906962 > 32⁸⁵ [i]