MinT - Best Known (33, 33+41, s)-Nets in Base 32

Best Known (33, 33+41, s)-Nets in Base 32

(33, 33+41, 174)-Net over F₃₂ — Constructive and digital

Digital (33, 74, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (33, 75, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 26, 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, 49, 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]

(33, 33+41, 288)-Net in Base 32 — Constructive

(33, 74, 288)-net in base 32, using

10 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 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]

(33, 33+41, 310)-Net over F₃₂ — Digital

Digital (33, 74, 310)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(33, 33+41, 342)-Net in Base 32

(33, 74, 342)-net in base 32, using

4 times m-reduction [i] based on (33, 78, 342)-net in base 32, using
- base change [i] based on digital (20, 65, 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]

(33, 33+41, 83500)-Net in Base 32 — Upper bound on s

There is no (33, 74, 83501)-net in base 32, because

1 times m-reduction [i] would yield (33, 73, 83501)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 75 161945 434908 890939 446499 584680 644071 493910 248904 042914 998623 372707 973969 908542 497862 117145 065205 753443 053526 > 32⁷³ [i]