MinT - Best Known (165, 165+66, s)-Nets in Base 3

Best Known (165, 165+66, s)-Nets in Base 3

(165, 165+66, 288)-Net over F₃ — Constructive and digital

Digital (165, 231, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 77, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(165, 165+66, 589)-Net over F₃ — Digital

Digital (165, 231, 589)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+66, 14361)-Net in Base 3 — Upper bound on s

There is no (165, 231, 14362)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 346688 023278 527737 184380 491031 369852 229672 644446 540713 964854 874058 187593 355232 432428 273224 420801 607859 633397 > 3²³¹ [i]