MinT - Best Known (118, 163, s)-Nets in Base 3

Best Known (118, 163, s)-Nets in Base 3

(118, 163, 264)-Net over F₃ — Constructive and digital

Digital (118, 163, 264)-net over F₃, using

3¹ times duplication [i] based on digital (117, 162, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 54, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(118, 163, 495)-Net over F₃ — Digital

Digital (118, 163, 495)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 163, 14741)-Net in Base 3 — Upper bound on s

There is no (118, 163, 14742)-net in base 3, because

1 times m-reduction [i] would yield (118, 162, 14742)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196811 316678 016763 319292 534512 434966 418836 313935 830154 486169 112210 404923 202133 > 3¹⁶² [i]