MinT - Best Known (86−57, 86, s)-Nets in Base 32

Best Known (86−57, 86, s)-Nets in Base 32

(86−57, 86, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 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]

(86−57, 86, 192)-Net in Base 32 — Constructive

(29, 86, 192)-net in base 32, using

5 times m-reduction [i] based on (29, 91, 192)-net in base 32, using
- base change [i] based on digital (3, 65, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(86−57, 86, 257)-Net over F₃₂ — Digital

Digital (29, 86, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 86, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(86−57, 86, 13501)-Net in Base 32 — Upper bound on s

There is no (29, 86, 13502)-net in base 32, because

1 times m-reduction [i] would yield (29, 85, 13502)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 86 715253 298844 478608 450699 521718 996219 315446 223404 144732 494945 679998 052723 706999 178640 743461 268829 662039 699356 089532 744985 090575 > 32⁸⁵ [i]