MinT - Best Known (224−125, 224, s)-Nets in Base 4

Best Known (224−125, 224, s)-Nets in Base 4

(224−125, 224, 104)-Net over F₄ — Constructive and digital

Digital (99, 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]

(224−125, 224, 144)-Net over F₄ — Digital

Digital (99, 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]

(224−125, 224, 1117)-Net in Base 4 — Upper bound on s

There is no (99, 224, 1118)-net in base 4, because

1 times m-reduction [i] would yield (99, 223, 1118)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 187 362677 338288 109387 500093 208319 777110 596178 344991 644613 023926 139549 684623 171964 964975 962078 218512 245090 259844 168605 577495 630616 622800 > 4²²³ [i]