MinT - Best Known (174−81, 174, s)-Nets in Base 4

Best Known (174−81, 174, s)-Nets in Base 4

(174−81, 174, 130)-Net over F₄ — Constructive and digital

Digital (93, 174, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 87, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(174−81, 174, 159)-Net over F₄ — Digital

Digital (93, 174, 159)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−81, 174, 2078)-Net in Base 4 — Upper bound on s

There is no (93, 174, 2079)-net in base 4, because

1 times m-reduction [i] would yield (93, 173, 2079)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 877866 371666 658150 739301 324741 631701 088974 813363 900099 604934 570466 462067 801118 883706 538812 041278 505792 > 4¹⁷³ [i]