MinT - Best Known (247−71, 247, s)-Nets in Base 3

Best Known (247−71, 247, s)-Nets in Base 3

(247−71, 247, 288)-Net over F₃ — Constructive and digital

Digital (176, 247, 288)-net over F₃, using

3¹ times duplication [i] based on digital (175, 246, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 82, 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]

(247−71, 247, 613)-Net over F₃ — Digital

Digital (176, 247, 613)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−71, 247, 15658)-Net in Base 3 — Upper bound on s

There is no (176, 247, 15659)-net in base 3, because

1 times m-reduction [i] would yield (176, 246, 15659)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2354 940613 053809 625141 772459 723924 327608 156898 247876 146260 932816 713032 921008 042971 521149 196431 466875 539035 678375 773835 > 3²⁴⁶ [i]