MinT - Best Known (22, 22+38, s)-Nets in Base 32

Best Known (22, 22+38, s)-Nets in Base 32

(22, 22+38, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 60, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 60, 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]

(22, 22+38, 185)-Net over F₃₂ — Digital

Digital (22, 60, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 60, 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]

(22, 22+38, 192)-Net in Base 32 — Constructive

(22, 60, 192)-net in base 32, using

6 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]

(22, 22+38, 257)-Net in Base 32

(22, 60, 257)-net in base 32, using

base change [i] based on digital (12, 50, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(22, 22+38, 14476)-Net in Base 32 — Upper bound on s

There is no (22, 60, 14477)-net in base 32, because

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]