MinT - Best Known (23, 23+39, s)-Nets in Base 32

Best Known (23, 23+39, s)-Nets in Base 32

Digital (23, 62, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 62, 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]

Digital (23, 62, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 62, 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]

(23, 62, 216)-net in base 32, using

1 times m-reduction [i] based on (23, 63, 216)-net in base 32, using
- base change [i] based on digital (5, 45, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(23, 62, 257)-net in base 32, using

4 times m-reduction [i] based on (23, 66, 257)-net in base 32, using
- base change [i] based on digital (12, 55, 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]

There is no (23, 62, 17376)-net in base 32, because

1 times m-reduction [i] would yield (23, 61, 17376)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 65 220947 632045 680391 018470 967706 024883 012733 250082 336418 497942 469891 718467 978263 952806 426143 > 32⁶¹ [i]