MinT - Best Known (60, 60+27, s)-Nets in Base 3

Best Known (60, 60+27, s)-Nets in Base 3

(60, 60+27, 144)-Net over F₃ — Constructive and digital

Digital (60, 87, 144)-net over F₃, using

trace code for nets [i] based on digital (2, 29, 48)-net over F₂₇, using
- net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
    - a function field by GarcÃa and Quoos [i]

(60, 60+27, 204)-Net over F₃ — Digital

Digital (60, 87, 204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+27, 4049)-Net in Base 3 — Upper bound on s

There is no (60, 87, 4050)-net in base 3, because

1 times m-reduction [i] would yield (60, 86, 4050)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107994 370685 705976 671936 411482 035202 897261 > 3⁸⁶ [i]