MinT - Best Known (89−64, 89, s)-Nets in Base 32

Best Known (89−64, 89, s)-Nets in Base 32

(89−64, 89, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(89−64, 89, 177)-Net in Base 32 — Constructive

(25, 89, 177)-net in base 32, using

19 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]

(89−64, 89, 225)-Net over F₃₂ — Digital

Digital (25, 89, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 89, 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]

(89−64, 89, 6318)-Net in Base 32 — Upper bound on s

There is no (25, 89, 6319)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 91 293823 679053 246032 946760 449687 959978 160326 351000 431355 061646 132271 213080 629856 667020 805161 595309 918708 679461 409224 820844 591521 573345 > 32⁸⁹ [i]