MinT - Best Known (136−51, 136, s)-Nets in Base 3

Best Known (136−51, 136, s)-Nets in Base 3

(136−51, 136, 148)-Net over F₃ — Constructive and digital

Digital (85, 136, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 68, 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]

(136−51, 136, 162)-Net over F₃ — Digital

Digital (85, 136, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−51, 136, 1894)-Net in Base 3 — Upper bound on s

There is no (85, 136, 1895)-net in base 3, because

1 times m-reduction [i] would yield (85, 135, 1895)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25946 133008 433574 155267 616822 285507 800833 042091 274848 573966 234783 > 3¹³⁵ [i]