MinT - Best Known (97−52, 97, s)-Nets in Base 16

Best Known (97−52, 97, s)-Nets in Base 16

Digital (45, 97, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 97, 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 (45, 97, 247)-net over F₁₆, using

(45, 97, 257)-net in base 16, using

2 times m-reduction [i] based on (45, 99, 257)-net in base 16, using
- base change [i] based on digital (12, 66, 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 (45, 97, 21838)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 630 440428 703180 927883 205007 848572 689675 350319 605119 588942 958083 829913 755805 825241 665153 402680 075268 146250 485483 108696 > 16⁹⁷ [i]