MinT - Best Known (220−125, 220, s)-Nets in Base 4

Best Known (220−125, 220, s)-Nets in Base 4

(220−125, 220, 104)-Net over F₄ — Constructive and digital

Digital (95, 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]

(220−125, 220, 144)-Net over F₄ — Digital

Digital (95, 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]

(220−125, 220, 1017)-Net in Base 4 — Upper bound on s

There is no (95, 220, 1018)-net in base 4, because

1 times m-reduction [i] would yield (95, 219, 1018)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 726824 322786 480963 345028 195236 086310 863102 648860 596524 230277 805434 177477 205846 974405 030662 489251 445762 111196 891648 339373 859350 704800 > 4²¹⁹ [i]