MinT - Best Known (154, 154+87, s)-Nets in Base 3

Best Known (154, 154+87, s)-Nets in Base 3

(154, 154+87, 162)-Net over F₃ — Constructive and digital

Digital (154, 241, 162)-net over F₃, using

3 times m-reduction [i] based on digital (154, 244, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 122, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(154, 154+87, 295)-Net over F₃ — Digital

Digital (154, 241, 295)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+87, 3843)-Net in Base 3 — Upper bound on s

There is no (154, 241, 3844)-net in base 3, because

1 times m-reduction [i] would yield (154, 240, 3844)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 260162 844032 142160 667653 978363 489819 014644 629222 831777 464179 487366 551457 219107 967588 615910 414075 348448 449193 195505 > 3²⁴⁰ [i]