MinT - Best Known (220−126, 220, s)-Nets in Base 4

Best Known (220−126, 220, s)-Nets in Base 4

(220−126, 220, 104)-Net over F₄ — Constructive and digital

Digital (94, 220, 104)-net over F₄, using

t-expansion [i] based on digital (73, 220, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(220−126, 220, 144)-Net over F₄ — Digital

Digital (94, 220, 144)-net over F₄, using

t-expansion [i] based on digital (91, 220, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(220−126, 220, 974)-Net in Base 4 — Upper bound on s

There is no (94, 220, 975)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 912100 454720 663382 561789 371868 613903 977469 670364 407343 706571 046547 576453 833861 443879 004637 045854 347055 072266 781118 996157 058886 801040 > 4²²⁰ [i]