MinT - Best Known (174, 174+70, s)-Nets in Base 3

Best Known (174, 174+70, s)-Nets in Base 3

(174, 174+70, 288)-Net over F₃ — Constructive and digital

Digital (174, 244, 288)-net over F₃, using

3¹ times duplication [i] based on digital (173, 243, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 81, 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]

(174, 174+70, 610)-Net over F₃ — Digital

Digital (174, 244, 610)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+70, 14703)-Net in Base 3 — Upper bound on s

There is no (174, 244, 14704)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 605850 927879 361233 947207 416896 189384 118032 555687 160802 881060 296837 093370 185554 346990 518166 180599 147266 781479 647681 > 3²⁴⁴ [i]