MinT - Best Known (89−49, 89, s)-Nets in Base 32

Best Known (89−49, 89, s)-Nets in Base 32

(89−49, 89, 202)-Net over F₃₂ — Constructive and digital

Digital (40, 89, 202)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 31, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (9, 58, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(89−49, 89, 288)-Net in Base 32 — Constructive

(40, 89, 288)-net in base 32, using

19 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
  - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
    - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(89−49, 89, 371)-Net over F₃₂ — Digital

Digital (40, 89, 371)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−49, 89, 408)-Net in Base 32

(40, 89, 408)-net in base 32, using

1 times m-reduction [i] based on (40, 90, 408)-net in base 32, using
- base change [i] based on digital (25, 75, 408)-net over F₆₄, using
  - net from sequence [i] based on digital (25, 407)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 25 and N(F) ≥ 408, using
      - a curve from the manYPoints database [i]

(89−49, 89, 104431)-Net in Base 32 — Upper bound on s

There is no (40, 89, 104432)-net in base 32, because

1 times m-reduction [i] would yield (40, 88, 104432)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 839266 901887 991951 886275 940703 295552 811698 628745 819838 137934 444324 488004 030535 514615 945915 952218 115686 274867 216193 162996 962391 943314 > 32⁸⁸ [i]