MinT - Best Known (142, 142+108, s)-Nets in Base 3

Best Known (142, 142+108, s)-Nets in Base 3

(142, 142+108, 148)-Net over F₃ — Constructive and digital

Digital (142, 250, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 125, 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]

(142, 142+108, 183)-Net over F₃ — Digital

Digital (142, 250, 183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+108, 1643)-Net in Base 3 — Upper bound on s

There is no (142, 250, 1644)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196098 278666 716350 121495 896796 877986 134622 954803 677334 222539 591720 121560 184916 947371 564035 016282 800947 644123 536045 290057 > 3²⁵⁰ [i]