MinT - Best Known (147, 147+55, s)-Nets in Base 3

Best Known (147, 147+55, s)-Nets in Base 3

(147, 147+55, 288)-Net over F₃ — Constructive and digital

Digital (147, 202, 288)-net over F₃, using

2 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+55, 621)-Net over F₃ — Digital

Digital (147, 202, 621)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+55, 19439)-Net in Base 3 — Upper bound on s

There is no (147, 202, 19440)-net in base 3, because

1 times m-reduction [i] would yield (147, 201, 19440)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797242 817171 687821 455584 305392 211582 150711 386052 402714 173380 797367 496633 818424 809080 694810 990017 > 3²⁰¹ [i]