MinT - Best Known (168−49, 168, s)-Nets in Base 3

Best Known (168−49, 168, s)-Nets in Base 3

(168−49, 168, 246)-Net over F₃ — Constructive and digital

Digital (119, 168, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 56, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(168−49, 168, 419)-Net over F₃ — Digital

Digital (119, 168, 419)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−49, 168, 10216)-Net in Base 3 — Upper bound on s

There is no (119, 168, 10217)-net in base 3, because

1 times m-reduction [i] would yield (119, 167, 10217)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 829868 336415 479957 316663 275277 547872 237614 491048 207465 308362 915071 604024 755681 > 3¹⁶⁷ [i]