MinT - Best Known (119, 119+45, s)-Nets in Base 3

Best Known (119, 119+45, s)-Nets in Base 3

(119, 119+45, 264)-Net over F₃ — Constructive and digital

Digital (119, 164, 264)-net over F₃, using

1 times m-reduction [i] based on digital (119, 165, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 55, 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]

(119, 119+45, 508)-Net over F₃ — Digital

Digital (119, 164, 508)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+45, 15497)-Net in Base 3 — Upper bound on s

There is no (119, 164, 15498)-net in base 3, because

1 times m-reduction [i] would yield (119, 163, 15498)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 590466 961645 396543 058924 911246 334305 008806 548269 903090 896731 984119 863210 519437 > 3¹⁶³ [i]