MinT - Best Known (174, 174+78, s)-Nets in Base 4

Best Known (174, 174+78, s)-Nets in Base 4

(174, 174+78, 486)-Net over F₄ — Constructive and digital

Digital (174, 252, 486)-net over F₄, using

trace code for nets [i] based on digital (48, 126, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(174, 174+78, 893)-Net over F₄ — Digital

Digital (174, 252, 893)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+78, 39828)-Net in Base 4 — Upper bound on s

There is no (174, 252, 39829)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 422662 247246 199066 771471 444212 290796 859311 871050 061190 008873 603926 131287 477047 888039 667946 105036 302198 622779 540664 528612 927327 992503 554981 392788 020032 > 4²⁵² [i]