MinT - Best Known (62, 89, s)-Nets in Base 3

Best Known (62, 89, s)-Nets in Base 3

(62, 89, 148)-Net over F₃ — Constructive and digital

Digital (62, 89, 148)-net over F₃, using

1 times m-reduction [i] based on digital (62, 90, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 45, 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]

(62, 89, 224)-Net over F₃ — Digital

Digital (62, 89, 224)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 89, 4797)-Net in Base 3 — Upper bound on s

There is no (62, 89, 4798)-net in base 3, because

1 times m-reduction [i] would yield (62, 88, 4798)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 971776 774604 453632 089050 421942 891673 023621 > 3⁸⁸ [i]