MinT - Best Known (86, 86+31, s)-Nets in Base 3

Best Known (86, 86+31, s)-Nets in Base 3

(86, 86+31, 252)-Net over F₃ — Constructive and digital

Digital (86, 117, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 39, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(86, 86+31, 448)-Net over F₃ — Digital

Digital (86, 117, 448)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+31, 15706)-Net in Base 3 — Upper bound on s

There is no (86, 117, 15707)-net in base 3, because

1 times m-reduction [i] would yield (86, 116, 15707)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 200241 763736 140223 835725 979292 686876 146500 961280 281171 > 3¹¹⁶ [i]