MinT - Best Known (92, 92+116, s)-Nets in Base 4

Best Known (92, 92+116, s)-Nets in Base 4

(92, 92+116, 104)-Net over F₄ — Constructive and digital

Digital (92, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(92, 92+116, 144)-Net over F₄ — Digital

Digital (92, 208, 144)-net over F₄, using

t-expansion [i] based on digital (91, 208, 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]

(92, 92+116, 1032)-Net in Base 4 — Upper bound on s

There is no (92, 208, 1033)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 174350 220434 023132 812794 957608 060424 934265 899535 604011 961774 198041 018621 640312 680335 726984 258552 343215 374218 161817 421460 467200 > 4²⁰⁸ [i]