MinT - Best Known (67, 67+53, s)-Nets in Base 3

Best Known (67, 67+53, s)-Nets in Base 3

(67, 67+53, 72)-Net over F₃ — Constructive and digital

Digital (67, 120, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 60, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(67, 67+53, 92)-Net over F₃ — Digital

Digital (67, 120, 92)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+53, 780)-Net in Base 3 — Upper bound on s

There is no (67, 120, 781)-net in base 3, because

1 times m-reduction [i] would yield (67, 119, 781)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 614 092006 920519 551741 279735 116514 110404 690425 418993 419265 > 3¹¹⁹ [i]