MinT - Best Known (86, 86+51, s)-Nets in Base 3

Best Known (86, 86+51, s)-Nets in Base 3

(86, 86+51, 148)-Net over F₃ — Constructive and digital

Digital (86, 137, 148)-net over F₃, using

1 times m-reduction [i] based on digital (86, 138, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 69, 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]

(86, 86+51, 166)-Net over F₃ — Digital

Digital (86, 137, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+51, 1980)-Net in Base 3 — Upper bound on s

There is no (86, 137, 1981)-net in base 3, because

1 times m-reduction [i] would yield (86, 136, 1981)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77624 323971 339412 375370 035425 569748 808733 549148 455873 783980 863771 > 3¹³⁶ [i]