MinT - Best Known (84, 84+45, s)-Nets in Base 3

Best Known (84, 84+45, s)-Nets in Base 3

(84, 84+45, 148)-Net over F₃ — Constructive and digital

Digital (84, 129, 148)-net over F₃, using

5 times m-reduction [i] based on 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]

(84, 84+45, 193)-Net over F₃ — Digital

Digital (84, 129, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+45, 2681)-Net in Base 3 — Upper bound on s

There is no (84, 129, 2682)-net in base 3, because

1 times m-reduction [i] would yield (84, 128, 2682)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 858284 075646 884873 577323 599223 476368 144216 628881 957199 616557 > 3¹²⁸ [i]