MinT - Best Known (172, 172+73, s)-Nets in Base 3

Best Known (172, 172+73, s)-Nets in Base 3

(172, 172+73, 252)-Net over F₃ — Constructive and digital

Digital (172, 245, 252)-net over F₃, using

1 times m-reduction [i] based on digital (172, 246, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 82, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(172, 172+73, 541)-Net over F₃ — Digital

Digital (172, 245, 541)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+73, 12197)-Net in Base 3 — Upper bound on s

There is no (172, 245, 12198)-net in base 3, because

1 times m-reduction [i] would yield (172, 244, 12198)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 262 008834 087899 813352 262282 449403 460831 553735 399578 161306 165338 458060 482102 160467 735373 645057 507159 932318 910248 516169 > 3²⁴⁴ [i]