MinT - Best Known (138, 138+99, s)-Nets in Base 3

Best Known (138, 138+99, s)-Nets in Base 3

(138, 138+99, 148)-Net over F₃ — Constructive and digital

Digital (138, 237, 148)-net over F₃, using

5 times m-reduction [i] based on digital (138, 242, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 121, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(138, 138+99, 192)-Net over F₃ — Digital

Digital (138, 237, 192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+99, 1849)-Net in Base 3 — Upper bound on s

There is no (138, 237, 1850)-net in base 3, because

1 times m-reduction [i] would yield (138, 236, 1850)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40065 266667 174639 793731 601323 748455 423645 957324 059625 286870 151537 872686 289493 976737 956389 988322 260553 408255 438229 > 3²³⁶ [i]