MinT - Best Known (145, 145+81, s)-Nets in Base 3

Best Known (145, 145+81, s)-Nets in Base 3

(145, 145+81, 162)-Net over F₃ — Constructive and digital

Digital (145, 226, 162)-net over F₃, using

trace code for nets [i] based on digital (32, 113, 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]

(145, 145+81, 285)-Net over F₃ — Digital

Digital (145, 226, 285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+81, 3767)-Net in Base 3 — Upper bound on s

There is no (145, 226, 3768)-net in base 3, because

1 times m-reduction [i] would yield (145, 225, 3768)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 226138 737692 279299 391008 223797 801075 420097 228035 994490 349747 560245 155639 968920 807124 355047 161764 995422 189825 > 3²²⁵ [i]