MinT - Best Known (42, 101, s)-Nets in Base 32

Best Known (42, 101, s)-Nets in Base 32

(42, 101, 174)-Net over F₃₂ — Constructive and digital

Digital (42, 101, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (42, 102, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 35, 76)-net over F₃₂, using
    - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
        a function field by SÃ©mirat [i]
  2. digital (7, 67, 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]

(42, 101, 288)-Net in Base 32 — Constructive

(42, 101, 288)-net in base 32, using

t-expansion [i] based on (40, 101, 288)-net in base 32, using
- 7 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]

(42, 101, 308)-Net over F₃₂ — Digital

Digital (42, 101, 308)-net over F₃₂, using

t-expansion [i] based on digital (41, 101, 308)-net over F₃₂, using
- net from sequence [i] based on digital (41, 307)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 41 and N(F) ≥ 308, using
    - a curve from the manYPoints database [i]

(42, 101, 408)-Net in Base 32

(42, 101, 408)-net in base 32, using

1 times m-reduction [i] based on (42, 102, 408)-net in base 32, using
- base change [i] based on digital (25, 85, 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]

(42, 101, 58320)-Net in Base 32 — Upper bound on s

There is no (42, 101, 58321)-net in base 32, because

1 times m-reduction [i] would yield (42, 100, 58321)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 274152 886232 299900 900931 615957 360952 338584 232010 117656 876072 410884 975177 511725 764172 736275 820124 903288 087749 362017 180637 516961 254739 788882 348420 004544 > 32¹⁰⁰ [i]