MinT - Best Known (84, 135, s)-Nets in Base 3

Best Known (84, 135, s)-Nets in Base 3

(84, 135, 128)-Net over F₃ — Constructive and digital

Digital (84, 135, 128)-net over F₃, using

7 times m-reduction [i] based on digital (84, 142, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 71, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(84, 135, 158)-Net over F₃ — Digital

Digital (84, 135, 158)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 135, 1812)-Net in Base 3 — Upper bound on s

There is no (84, 135, 1813)-net in base 3, because

1 times m-reduction [i] would yield (84, 134, 1813)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8709 368180 212378 910272 139667 651994 337506 683776 584866 907784 727627 > 3¹³⁴ [i]