MinT - Best Known (119, 119+51, s)-Nets in Base 3

Best Known (119, 119+51, s)-Nets in Base 3

(119, 119+51, 204)-Net over F₃ — Constructive and digital

Digital (119, 170, 204)-net over F₃, using

1 times m-reduction [i] based on digital (119, 171, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 57, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(119, 119+51, 385)-Net over F₃ — Digital

Digital (119, 170, 385)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+51, 8524)-Net in Base 3 — Upper bound on s

There is no (119, 170, 8525)-net in base 3, because

1 times m-reduction [i] would yield (119, 169, 8525)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430 115313 420335 594452 631718 945197 950832 818775 255897 489502 335555 594288 882603 778363 > 3¹⁶⁹ [i]