MinT - Best Known (224−126, 224, s)-Nets in Base 4

Best Known (224−126, 224, s)-Nets in Base 4

(224−126, 224, 104)-Net over F₄ — Constructive and digital

Digital (98, 224, 104)-net over F₄, using

t-expansion [i] based on digital (73, 224, 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]

(224−126, 224, 144)-Net over F₄ — Digital

Digital (98, 224, 144)-net over F₄, using

t-expansion [i] based on digital (91, 224, 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]

(224−126, 224, 1068)-Net in Base 4 — Upper bound on s

There is no (98, 224, 1069)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 732 112991 096552 381470 235497 191641 954703 642516 344990 041845 698361 501146 571091 788563 826065 089834 073790 180529 450836 787391 671007 681282 667520 > 4²²⁴ [i]