MinT - Best Known (205−87, 205, s)-Nets in Base 3

Best Known (205−87, 205, s)-Nets in Base 3

(205−87, 205, 128)-Net over F₃ — Constructive and digital

Digital (118, 205, 128)-net over F₃, using

5 times m-reduction [i] based on digital (118, 210, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 105, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(205−87, 205, 162)-Net over F₃ — Digital

Digital (118, 205, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−87, 205, 1506)-Net in Base 3 — Upper bound on s

There is no (118, 205, 1507)-net in base 3, because

1 times m-reduction [i] would yield (118, 204, 1507)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 657202 346849 840501 429172 256108 452925 833563 959834 923578 441089 163585 880348 229384 636841 191960 401243 > 3²⁰⁴ [i]