MinT - Best Known (108−75, 108, s)-Nets in Base 32

Best Known (108−75, 108, s)-Nets in Base 32

(108−75, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(108−75, 108, 177)-Net in Base 32 — Constructive

(33, 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]

(108−75, 108, 273)-Net over F₃₂ — Digital

Digital (33, 108, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 108, 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]

(108−75, 108, 10629)-Net in Base 32 — Upper bound on s

There is no (33, 108, 10630)-net in base 32, because

1 times m-reduction [i] would yield (33, 107, 10630)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112811 464576 430605 756934 883242 229067 568725 668267 606645 161937 315634 327262 917729 215347 855309 289600 111709 973259 727548 287717 955664 348450 710261 081103 026134 674564 293388 > 32¹⁰⁷ [i]