MinT - Best Known (119, 119+41, s)-Nets in Base 3

Best Known (119, 119+41, s)-Nets in Base 3

(119, 119+41, 288)-Net over F₃ — Constructive and digital

Digital (119, 160, 288)-net over F₃, using

2 times m-reduction [i] based on digital (119, 162, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 54, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(119, 119+41, 645)-Net over F₃ — Digital

Digital (119, 160, 645)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+41, 25766)-Net in Base 3 — Upper bound on s

There is no (119, 160, 25767)-net in base 3, because

1 times m-reduction [i] would yield (119, 159, 25767)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7283 182729 269939 316839 326032 139569 942923 202624 501365 699620 893455 148834 849113 > 3¹⁵⁹ [i]