MinT - Best Known (44, 99, s)-Nets in Base 32

Best Known (44, 99, s)-Nets in Base 32

(44, 99, 202)-Net over F₃₂ — Constructive and digital

Digital (44, 99, 202)-net over F₃₂, using

1 times m-reduction [i] based on digital (44, 100, 202)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 35, 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, 65, 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]

(44, 99, 288)-Net in Base 32 — Constructive

(44, 99, 288)-net in base 32, using

t-expansion [i] based on (40, 99, 288)-net in base 32, using
- 9 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]

(44, 99, 382)-Net over F₃₂ — Digital

Digital (44, 99, 382)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 99, 425)-Net in Base 32

(44, 99, 425)-net in base 32, using

9 times m-reduction [i] based on (44, 108, 425)-net in base 32, using
- base change [i] based on digital (26, 90, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(44, 99, 102358)-Net in Base 32 — Upper bound on s

There is no (44, 99, 102359)-net in base 32, because

1 times m-reduction [i] would yield (44, 98, 102359)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3197 236292 535871 076844 820393 863350 121390 501096 544633 221428 586224 113942 298075 039345 629318 145041 816912 919012 146424 474286 360802 531401 019403 066013 567904 > 32⁹⁸ [i]