MinT - Best Known (96, 96+124, s)-Nets in Base 4

Best Known (96, 96+124, s)-Nets in Base 4

(96, 96+124, 104)-Net over F₄ — Constructive and digital

Digital (96, 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]

(96, 96+124, 144)-Net over F₄ — Digital

Digital (96, 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]

(96, 96+124, 1041)-Net in Base 4 — Upper bound on s

There is no (96, 220, 1042)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 885081 283188 757812 750663 156330 681697 159554 153496 724541 789484 666445 835240 724497 125418 389162 075189 118820 297362 470650 843619 000676 185600 > 4²²⁰ [i]