MinT - Best Known (245−90, 245, s)-Nets in Base 3

Best Known (245−90, 245, s)-Nets in Base 3

(245−90, 245, 162)-Net over F₃ — Constructive and digital

Digital (155, 245, 162)-net over F₃, using

1 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 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]

(245−90, 245, 285)-Net over F₃ — Digital

Digital (155, 245, 285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−90, 245, 3445)-Net in Base 3 — Upper bound on s

There is no (155, 245, 3446)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 789 160034 920698 980819 089271 487425 582622 423913 193090 114382 040649 383812 541584 549121 347933 609475 022556 765841 969046 098677 > 3²⁴⁵ [i]