MinT - Best Known (26, 26+43, s)-Nets in Base 32

Best Known (26, 26+43, s)-Nets in Base 32

Digital (26, 69, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 69, 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]

(26, 69, 216)-net in base 32, using

Digital (26, 69, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 69, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(26, 69, 257)-net in base 32, using

15 times m-reduction [i] based on (26, 84, 257)-net in base 32, using
- base change [i] based on digital (12, 70, 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 (26, 69, 20929)-net in base 32, because

1 times m-reduction [i] would yield (26, 68, 20929)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 241923 859147 331462 643040 230115 158155 282211 799506 752386 338678 742107 685835 548084 281251 701896 735886 803520 > 32⁶⁸ [i]