MinT - Best Known (24, 24+42, s)-Nets in Base 32

Best Known (24, 24+42, s)-Nets in Base 32

Digital (24, 66, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 66, 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]

(24, 66, 216)-net in base 32, using

Digital (24, 66, 225)-net over F₃₂, using

(24, 66, 257)-net in base 32, using

6 times m-reduction [i] based on (24, 72, 257)-net in base 32, using
- base change [i] based on digital (12, 60, 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 (24, 66, 15042)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2188 464415 537866 254679 451892 048009 089631 346129 233613 256890 881233 511183 794727 340452 436973 897290 141296 > 32⁶⁶ [i]