MinT - Best Known (89, 89+64, s)-Nets in Base 3

Best Known (89, 89+64, s)-Nets in Base 3

(89, 89+64, 80)-Net over F₃ — Constructive and digital

Digital (89, 153, 80)-net over F₃, using

9 times m-reduction [i] based on digital (89, 162, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 81, 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]

(89, 89+64, 131)-Net over F₃ — Digital

Digital (89, 153, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+64, 1190)-Net in Base 3 — Upper bound on s

There is no (89, 153, 1191)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 021897 383420 064017 792524 731335 077510 683513 860645 005959 011989 600879 055297 > 3¹⁵³ [i]