MinT - Best Known (61−39, 61, s)-Nets in Base 32

Best Known (61−39, 61, s)-Nets in Base 32

(61−39, 61, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 61, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 61, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(61−39, 61, 185)-Net over F₃₂ — Digital

Digital (22, 61, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 61, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(61−39, 61, 192)-Net in Base 32 — Constructive

(22, 61, 192)-net in base 32, using

5 times m-reduction [i] based on (22, 66, 192)-net in base 32, using
- base change [i] based on (11, 55, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
    - base change [i] based on digital (3, 48, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(61−39, 61, 225)-Net in Base 32

(22, 61, 225)-net in base 32, using

11 times m-reduction [i] based on (22, 72, 225)-net in base 32, using
- base change [i] based on digital (10, 60, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(61−39, 61, 14476)-Net in Base 32 — Upper bound on s

There is no (22, 61, 14477)-net in base 32, because

1 times m-reduction [i] would yield (22, 60, 14477)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 037731 703757 236908 421065 754689 752291 416914 863454 421975 303757 166264 744939 683175 018110 037664 > 32⁶⁰ [i]