MinT - Best Known (155, 155+85, s)-Nets in Base 3

Best Known (155, 155+85, s)-Nets in Base 3

(155, 155+85, 162)-Net over F₃ — Constructive and digital

Digital (155, 240, 162)-net over F₃, using

6 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 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]

(155, 155+85, 311)-Net over F₃ — Digital

Digital (155, 240, 311)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+85, 4242)-Net in Base 3 — Upper bound on s

There is no (155, 240, 4243)-net in base 3, because

1 times m-reduction [i] would yield (155, 239, 4243)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 083121 201246 971626 284955 947508 180610 834486 453910 564466 551188 705957 065243 912047 898739 371532 005043 535831 723052 972085 > 3²³⁹ [i]