MinT - Best Known (174, 250, s)-Nets in Base 3

Best Known (174, 250, s)-Nets in Base 3

(174, 250, 246)-Net over F₃ — Constructive and digital

Digital (174, 250, 246)-net over F₃, using

3¹ times duplication [i] based on digital (173, 249, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 83, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(174, 250, 517)-Net over F₃ — Digital

Digital (174, 250, 517)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 250, 10307)-Net in Base 3 — Upper bound on s

There is no (174, 250, 10308)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 191022 891710 582843 303880 253503 822191 245233 079370 776058 325292 300873 627538 526002 189825 600697 900568 775331 994221 324405 396057 > 3²⁵⁰ [i]