MinT - Best Known (172, 172+78, s)-Nets in Base 3

Best Known (172, 172+78, s)-Nets in Base 3

(172, 172+78, 204)-Net over F₃ — Constructive and digital

Digital (172, 250, 204)-net over F₃, using

3¹ times duplication [i] based on digital (171, 249, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 83, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(172, 172+78, 476)-Net over F₃ — Digital

Digital (172, 250, 476)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+78, 8769)-Net in Base 3 — Upper bound on s

There is no (172, 250, 8770)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 191260 962009 156321 387352 833625 529578 728584 906019 661217 018708 288494 569735 722163 601912 372974 436668 416839 483379 510573 178921 > 3²⁵⁰ [i]