MinT - Best Known (172, 172+64, s)-Nets in Base 3

Best Known (172, 172+64, s)-Nets in Base 3

(172, 172+64, 288)-Net over F₃ — Constructive and digital

Digital (172, 236, 288)-net over F₃, using

t-expansion [i] based on digital (171, 236, 288)-net over F₃, using
- 4 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 80, 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]

(172, 172+64, 719)-Net over F₃ — Digital

Digital (172, 236, 719)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+64, 21084)-Net in Base 3 — Upper bound on s

There is no (172, 236, 21085)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39872 840784 950582 293176 438484 367352 906448 695116 952165 507441 852372 181929 314651 025243 836401 322703 837068 870931 807105 > 3²³⁶ [i]