MinT - Best Known (102−61, 102, s)-Nets in Base 32

Best Known (102−61, 102, s)-Nets in Base 32

(102−61, 102, 162)-Net over F₃₂ — Constructive and digital

Digital (41, 102, 162)-net over F₃₂, using

1 times m-reduction [i] based on digital (41, 103, 162)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (3, 34, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
  2. digital (7, 69, 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]

(102−61, 102, 288)-Net in Base 32 — Constructive

(41, 102, 288)-net in base 32, using

t-expansion [i] based on (40, 102, 288)-net in base 32, using
- 6 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]

(102−61, 102, 308)-Net over F₃₂ — Digital

Digital (41, 102, 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]

(102−61, 102, 342)-Net in Base 32

(41, 102, 342)-net in base 32, using

t-expansion [i] based on (38, 102, 342)-net in base 32, using
- 6 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
  - base change [i] based on digital (20, 90, 342)-net over F₆₄, using
    - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
        a curve from the manYPoints database [i]

(102−61, 102, 45354)-Net in Base 32 — Upper bound on s

There is no (41, 102, 45355)-net in base 32, because

1 times m-reduction [i] would yield (41, 101, 45355)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 104 806473 785674 342361 302065 525829 628061 080442 418684 554810 119244 650602 289596 162470 478023 918772 878252 784309 219251 579791 662298 580885 899274 449853 463858 406232 > 32¹⁰¹ [i]