MinT - Best Known (88−75, 88, s)-Nets in Base 32

Best Known (88−75, 88, s)-Nets in Base 32

(88−75, 88, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 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]

(88−75, 88, 129)-Net over F₃₂ — Digital

Digital (13, 88, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 88, 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]

(88−75, 88, 1616)-Net in Base 32 — Upper bound on s

There is no (13, 88, 1617)-net in base 32, because

1 times m-reduction [i] would yield (13, 87, 1617)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89754 150750 544991 818491 518654 634941 208885 595303 730343 785199 386672 778774 734025 361930 075813 786061 446987 236898 723471 606847 896533 384352 > 32⁸⁷ [i]