MinT - Best Known (186, 186+64, s)-Nets in Base 3

Best Known (186, 186+64, s)-Nets in Base 3

(186, 186+64, 324)-Net over F₃ — Constructive and digital

Digital (186, 250, 324)-net over F₃, using

3¹ times duplication [i] based on digital (185, 249, 324)-net over F₃, using
- t-expansion [i] based on digital (184, 249, 324)-net over F₃, using
  - trace code for nets [i] based on digital (18, 83, 108)-net over F₂₇, using
    - net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
        F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(186, 186+64, 934)-Net over F₃ — Digital

Digital (186, 250, 934)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+64, 34116)-Net in Base 3 — Upper bound on s

There is no (186, 250, 34117)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 190842 628710 005336 768012 667864 964077 752316 617313 390359 330816 661188 987354 165931 763207 040799 463826 292958 684049 998071 003009 > 3²⁵⁰ [i]