MinT - Best Known (46, 46+55, s)-Nets in Base 16

Best Known (46, 46+55, s)-Nets in Base 16

Digital (46, 101, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 101, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

Digital (46, 101, 243)-net over F₁₆, using

(46, 101, 257)-net in base 16, using

1 times m-reduction [i] based on (46, 102, 257)-net in base 16, using
- base change [i] based on digital (12, 68, 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 (46, 101, 20976)-net in base 16, because

1 times m-reduction [i] would yield (46, 100, 20976)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 583821 342743 331517 621128 837980 779795 077765 967876 478211 095978 518983 959630 053917 282325 160209 247857 238404 899643 257310 845506 > 16¹⁰⁰ [i]