MinT - Best Known (92−79, 92, s)-Nets in Base 32

Best Known (92−79, 92, s)-Nets in Base 32

(92−79, 92, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 92, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 92, 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]

(92−79, 92, 129)-Net over F₃₂ — Digital

Digital (13, 92, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 92, 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]

(92−79, 92, 1594)-Net in Base 32 — Upper bound on s

There is no (13, 92, 1595)-net in base 32, because

1 times m-reduction [i] would yield (13, 91, 1595)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 94272 650071 839203 457544 394344 467630 138254 694223 557700 470935 780440 918974 031865 765353 705379 083895 177951 264879 536267 834855 326712 724934 662440 > 32⁹¹ [i]