MinT - Best Known (119, 171, s)-Nets in Base 3

Best Known (119, 171, s)-Nets in Base 3

(119, 171, 204)-Net over F₃ — Constructive and digital

Digital (119, 171, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 57, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(119, 171, 371)-Net over F₃ — Digital

Digital (119, 171, 371)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 171, 7223)-Net in Base 3 — Upper bound on s

There is no (119, 171, 7224)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3882 504529 641962 520729 202819 209816 950352 267093 101336 048451 511691 293888 141029 938001 > 3¹⁷¹ [i]