MinT - Best Known (134−50, 134, s)-Nets in Base 3

Best Known (134−50, 134, s)-Nets in Base 3

(134−50, 134, 148)-Net over F₃ — Constructive and digital

Digital (84, 134, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 67, 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]

(134−50, 134, 162)-Net over F₃ — Digital

Digital (84, 134, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−50, 134, 1812)-Net in Base 3 — Upper bound on s

There is no (84, 134, 1813)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8709 368180 212378 910272 139667 651994 337506 683776 584866 907784 727627 > 3¹³⁴ [i]