MinT - Best Known (85, 85+67, s)-Nets in Base 3

Best Known (85, 85+67, s)-Nets in Base 3

(85, 85+67, 80)-Net over F₃ — Constructive and digital

Digital (85, 152, 80)-net over F₃, using

2 times m-reduction [i] based on digital (85, 154, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 77, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(85, 85+67, 113)-Net over F₃ — Digital

Digital (85, 152, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+67, 971)-Net in Base 3 — Upper bound on s

There is no (85, 152, 972)-net in base 3, because

1 times m-reduction [i] would yield (85, 151, 972)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 131076 506221 878704 525306 198499 796109 934006 959183 162675 131319 589648 904089 > 3¹⁵¹ [i]