MinT - Best Known (138, 138+103, s)-Nets in Base 3

Best Known (138, 138+103, s)-Nets in Base 3

(138, 138+103, 148)-Net over F₃ — Constructive and digital

Digital (138, 241, 148)-net over F₃, using

1 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+103, 183)-Net over F₃ — Digital

Digital (138, 241, 183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+103, 1696)-Net in Base 3 — Upper bound on s

There is no (138, 241, 1697)-net in base 3, because

1 times m-reduction [i] would yield (138, 240, 1697)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 292773 407506 577491 946255 164012 282952 846461 112716 236756 536322 630619 334477 810152 515363 359342 985098 506351 050777 348315 > 3²⁴⁰ [i]