MinT - Best Known (92, 92+104, s)-Nets in Base 4

Best Known (92, 92+104, s)-Nets in Base 4

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

Digital (92, 196, 104)-net over F₄, using

t-expansion [i] based on digital (73, 196, 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+104, 144)-Net over F₄ — Digital

Digital (92, 196, 144)-net over F₄, using

t-expansion [i] based on digital (91, 196, 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+104, 1211)-Net in Base 4 — Upper bound on s

There is no (92, 196, 1212)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10477 035818 153635 053658 336038 749491 869899 904709 041403 589673 396934 051737 881826 565885 145227 368328 498358 311331 419266 962350 > 4¹⁹⁶ [i]