MinT - Best Known (54, 54+44, s)-Nets in Base 3

Best Known (54, 54+44, s)-Nets in Base 3

(54, 54+44, 64)-Net over F₃ — Constructive and digital

Digital (54, 98, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 49, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(54, 54+44, 75)-Net over F₃ — Digital

Digital (54, 98, 75)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+44, 583)-Net in Base 3 — Upper bound on s

There is no (54, 98, 584)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 59355 035684 565885 116901 399578 342373 431485 612209 > 3⁹⁸ [i]