MinT - Best Known (120, 206, s)-Nets in Base 3

Best Known (120, 206, s)-Nets in Base 3

(120, 206, 148)-Net over F₃ — Constructive and digital

Digital (120, 206, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 103, 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]

(120, 206, 170)-Net over F₃ — Digital

Digital (120, 206, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 206, 1587)-Net in Base 3 — Upper bound on s

There is no (120, 206, 1588)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 961300 221701 127426 947182 559321 470731 175474 572509 917846 057365 226835 033005 300770 588104 585998 291889 > 3²⁰⁶ [i]