MinT - Best Known (170, 246, s)-Nets in Base 3

Best Known (170, 246, s)-Nets in Base 3

(170, 246, 228)-Net over F₃ — Constructive and digital

Digital (170, 246, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 82, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(170, 246, 485)-Net over F₃ — Digital

Digital (170, 246, 485)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 246, 9177)-Net in Base 3 — Upper bound on s

There is no (170, 246, 9178)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2356 263302 152921 773640 381421 652664 997544 674096 495356 821890 073627 197084 783468 018161 049763 053135 990167 682314 169157 743373 > 3²⁴⁶ [i]