MinT - Best Known (186−76, 186, s)-Nets in Base 3

Best Known (186−76, 186, s)-Nets in Base 3

(186−76, 186, 148)-Net over F₃ — Constructive and digital

Digital (110, 186, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 93, 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]

(186−76, 186, 165)-Net over F₃ — Digital

Digital (110, 186, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−76, 186, 1588)-Net in Base 3 — Upper bound on s

There is no (110, 186, 1589)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55546 416966 905772 561251 245898 734660 928512 292210 284821 788492 556566 530776 640107 303323 720865 > 3¹⁸⁶ [i]