MinT - Best Known (88, 119, s)-Nets in Base 3

Best Known (88, 119, s)-Nets in Base 3

(88, 119, 252)-Net over F₃ — Constructive and digital

Digital (88, 119, 252)-net over F₃, using

1 times m-reduction [i] based on digital (88, 120, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 40, 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]

(88, 119, 485)-Net over F₃ — Digital

Digital (88, 119, 485)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 119, 18186)-Net in Base 3 — Upper bound on s

There is no (88, 119, 18187)-net in base 3, because

1 times m-reduction [i] would yield (88, 118, 18187)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199 781970 658804 820903 936295 824831 498901 405359 810912 833811 > 3¹¹⁸ [i]