MinT - Best Known (220−129, 220, s)-Nets in Base 4

Best Known (220−129, 220, s)-Nets in Base 4

(220−129, 220, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(220−129, 220, 144)-Net over F₄ — Digital

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]

(220−129, 220, 892)-Net in Base 4 — Upper bound on s

There is no (91, 220, 893)-net in base 4, because

1 times m-reduction [i] would yield (91, 219, 893)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 711617 340979 454466 408800 115635 257507 879734 793149 156854 060947 411999 330762 335753 264291 776102 503610 909063 808619 116642 473646 080702 386975 > 4²¹⁹ [i]