MinT - Best Known (147, 147+53, s)-Nets in Base 3

Best Known (147, 147+53, s)-Nets in Base 3

(147, 147+53, 288)-Net over F₃ — Constructive and digital

Digital (147, 200, 288)-net over F₃, using

4 times m-reduction [i] based on digital (147, 204, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 68, 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]

(147, 147+53, 680)-Net over F₃ — Digital

Digital (147, 200, 680)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+53, 23637)-Net in Base 3 — Upper bound on s

There is no (147, 200, 23638)-net in base 3, because

1 times m-reduction [i] would yield (147, 199, 23638)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88554 139819 209954 574164 944779 978226 786314 319094 853427 903780 180005 094203 333816 383931 109751 010941 > 3¹⁹⁹ [i]