MinT - Best Known (117−49, 117, s)-Nets in Base 3

Best Known (117−49, 117, s)-Nets in Base 3

(117−49, 117, 80)-Net over F₃ — Constructive and digital

Digital (68, 117, 80)-net over F₃, using

3 times m-reduction [i] based on digital (68, 120, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 60, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(117−49, 117, 105)-Net over F₃ — Digital

Digital (68, 117, 105)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−49, 117, 968)-Net in Base 3 — Upper bound on s

There is no (68, 117, 969)-net in base 3, because

1 times m-reduction [i] would yield (68, 116, 969)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 445723 404786 541243 217238 204001 032745 441226 665766 346209 > 3¹¹⁶ [i]