MinT - Best Known (58−45, 58, s)-Nets in Base 32

Best Known (58−45, 58, s)-Nets in Base 32

(58−45, 58, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 58, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 58, 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]

(58−45, 58, 129)-Net over F₃₂ — Digital

Digital (13, 58, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 58, 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]

(58−45, 58, 2307)-Net in Base 32 — Upper bound on s

There is no (13, 58, 2308)-net in base 32, because

1 times m-reduction [i] would yield (13, 57, 2308)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 62 606816 453034 419136 219295 932310 940491 085457 172939 785682 706850 900970 287175 298559 424704 > 32⁵⁷ [i]