MinT - Best Known (194−96, 194, s)-Nets in Base 4

Best Known (194−96, 194, s)-Nets in Base 4

(194−96, 194, 104)-Net over F₄ — Constructive and digital

Digital (98, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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]

(194−96, 194, 145)-Net over F₄ — Digital

Digital (98, 194, 145)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−96, 194, 1655)-Net in Base 4 — Upper bound on s

There is no (98, 194, 1656)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645 545070 304751 380564 734961 110209 404593 935142 281849 497038 353903 518182 100548 447146 640985 548269 635012 956574 430693 504527 > 4¹⁹⁴ [i]