MinT - Best Known (138−52, 138, s)-Nets in Base 3

Best Known (138−52, 138, s)-Nets in Base 3

(138−52, 138, 148)-Net over F₃ — Constructive and digital

Digital (86, 138, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 69, 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]

(138−52, 138, 162)-Net over F₃ — Digital

Digital (86, 138, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−52, 138, 1772)-Net in Base 3 — Upper bound on s

There is no (86, 138, 1773)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 704515 610763 591857 065708 564571 588151 386586 077990 120253 417469 695681 > 3¹³⁸ [i]