MinT - Best Known (215−70, 215, s)-Nets in Base 3

Best Known (215−70, 215, s)-Nets in Base 3

(215−70, 215, 162)-Net over F₃ — Constructive and digital

Digital (145, 215, 162)-net over F₃, using

11 times m-reduction [i] based on digital (145, 226, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 113, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(215−70, 215, 365)-Net over F₃ — Digital

Digital (145, 215, 365)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−70, 215, 5896)-Net in Base 3 — Upper bound on s

There is no (145, 215, 5897)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 822625 835453 872171 289413 172183 942095 205974 726007 549005 516850 601144 973502 373974 392173 489031 744724 926203 > 3²¹⁵ [i]