MinT - Best Known (174−55, 174, s)-Nets in Base 3

Best Known (174−55, 174, s)-Nets in Base 3

(174−55, 174, 162)-Net over F₃ — Constructive and digital

Digital (119, 174, 162)-net over F₃, using

trace code for nets [i] based on digital (32, 87, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(174−55, 174, 334)-Net over F₃ — Digital

Digital (119, 174, 334)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−55, 174, 6203)-Net in Base 3 — Upper bound on s

There is no (119, 174, 6204)-net in base 3, because

1 times m-reduction [i] would yield (119, 173, 6204)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34902 531745 401621 350841 502251 312413 221689 302924 480592 156082 500635 677005 583277 391953 > 3¹⁷³ [i]