MinT - Best Known (105−62, 105, s)-Nets in Base 32

Best Known (105−62, 105, s)-Nets in Base 32

(105−62, 105, 174)-Net over F₃₂ — Constructive and digital

Digital (43, 105, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 36, 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, 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]

(105−62, 105, 288)-Net in Base 32 — Constructive

(43, 105, 288)-net in base 32, using

t-expansion [i] based on (40, 105, 288)-net in base 32, using
- 3 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]

(105−62, 105, 308)-Net over F₃₂ — Digital

Digital (43, 105, 308)-net over F₃₂, using

t-expansion [i] based on digital (41, 105, 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]

(105−62, 105, 408)-Net in Base 32

(43, 105, 408)-net in base 32, using

3 times m-reduction [i] based on (43, 108, 408)-net in base 32, using
- base change [i] based on digital (25, 90, 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]

(105−62, 105, 50190)-Net in Base 32 — Upper bound on s

There is no (43, 105, 50191)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 109 870948 349464 628817 101492 784764 811323 435853 632790 089817 665727 808953 088948 586515 899622 089247 578917 472331 419081 824041 628516 693583 450449 316493 451440 557792 691200 > 32¹⁰⁵ [i]