MinT - Best Known (156, 156+85, s)-Nets in Base 3

Best Known (156, 156+85, s)-Nets in Base 3

(156, 156+85, 162)-Net over F₃ — Constructive and digital

Digital (156, 241, 162)-net over F₃, using

7 times m-reduction [i] based on digital (156, 248, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 124, 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]

(156, 156+85, 316)-Net over F₃ — Digital

Digital (156, 241, 316)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+85, 4355)-Net in Base 3 — Upper bound on s

There is no (156, 241, 4356)-net in base 3, because

1 times m-reduction [i] would yield (156, 240, 4356)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 232603 662635 921616 770451 355618 898251 014800 990598 208809 860863 076510 109890 628875 037201 904067 543983 091952 327119 425209 > 3²⁴⁰ [i]