MinT - Best Known (173−53, 173, s)-Nets in Base 3

Best Known (173−53, 173, s)-Nets in Base 3

(173−53, 173, 192)-Net over F₃ — Constructive and digital

Digital (120, 173, 192)-net over F₃, using

1 times m-reduction [i] based on digital (120, 174, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 58, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(173−53, 173, 366)-Net over F₃ — Digital

Digital (120, 173, 366)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−53, 173, 7535)-Net in Base 3 — Upper bound on s

There is no (120, 173, 7536)-net in base 3, because

1 times m-reduction [i] would yield (120, 172, 7536)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11612 190135 665743 484233 186363 506350 366058 494558 169887 999025 523546 405765 917972 669345 > 3¹⁷² [i]