MinT - Best Known (86−61, 86, s)-Nets in Base 32

Best Known (86−61, 86, s)-Nets in Base 32

(86−61, 86, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 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]

(86−61, 86, 177)-Net in Base 32 — Constructive

(25, 86, 177)-net in base 32, using

22 times m-reduction [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]

(86−61, 86, 225)-Net over F₃₂ — Digital

Digital (25, 86, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 86, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(86−61, 86, 7129)-Net in Base 32 — Upper bound on s

There is no (25, 86, 7130)-net in base 32, because

1 times m-reduction [i] would yield (25, 85, 7130)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 86 715629 059765 356101 372140 816262 864750 186073 060509 440435 546813 028821 553541 412365 351692 291383 254478 933208 702630 816185 401090 335584 > 32⁸⁵ [i]