MinT - Best Known (120, 120+115, s)-Nets in Base 3

Best Known (120, 120+115, s)-Nets in Base 3

(120, 120+115, 77)-Net over F₃ — Constructive and digital

Digital (120, 235, 77)-net over F₃, using

net from sequence [i] based on digital (120, 76)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 76)-sequence over F₉, using
  - s-reduction based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(120, 120+115, 122)-Net over F₃ — Digital

Digital (120, 235, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+115, 948)-Net in Base 3 — Upper bound on s

There is no (120, 235, 949)-net in base 3, because

1 times m-reduction [i] would yield (120, 234, 949)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4519 346832 892582 811775 111836 059265 077286 441385 450324 602898 192500 476240 228412 797206 144423 369291 948635 353375 673099 > 3²³⁴ [i]