MinT - Best Known (221−133, 221, s)-Nets in Base 4

Best Known (221−133, 221, s)-Nets in Base 4

(221−133, 221, 104)-Net over F₄ — Constructive and digital

Digital (88, 221, 104)-net over F₄, using

t-expansion [i] based on digital (73, 221, 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]

(221−133, 221, 129)-Net over F₄ — Digital

Digital (88, 221, 129)-net over F₄, using

t-expansion [i] based on digital (81, 221, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(221−133, 221, 807)-Net in Base 4 — Upper bound on s

There is no (88, 221, 808)-net in base 4, because

1 times m-reduction [i] would yield (88, 220, 808)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 963744 193251 796600 592720 400709 604525 847173 600708 633159 408835 088627 024826 773825 030961 896898 377535 052737 272330 332199 262440 342131 015500 > 4²²⁰ [i]