MinT - Best Known (119, 119+85, s)-Nets in Base 3

Best Known (119, 119+85, s)-Nets in Base 3

(119, 119+85, 148)-Net over F₃ — Constructive and digital

Digital (119, 204, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 102, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(119, 119+85, 169)-Net over F₃ — Digital

Digital (119, 204, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+85, 1629)-Net in Base 3 — Upper bound on s

There is no (119, 204, 1630)-net in base 3, because

1 times m-reduction [i] would yield (119, 203, 1630)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 268052 865616 084298 498244 772972 022583 032552 331471 984179 364722 028201 206985 711932 899232 334773 306381 > 3²⁰³ [i]