MinT - Best Known (246−89, 246, s)-Nets in Base 3

Best Known (246−89, 246, s)-Nets in Base 3

(246−89, 246, 162)-Net over F₃ — Constructive and digital

Digital (157, 246, 162)-net over F₃, using

4 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 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]

(246−89, 246, 299)-Net over F₃ — Digital

Digital (157, 246, 299)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−89, 246, 3870)-Net in Base 3 — Upper bound on s

There is no (157, 246, 3871)-net in base 3, because

1 times m-reduction [i] would yield (157, 245, 3871)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 789 765950 675810 837296 654228 231402 367402 681982 718796 837718 999743 615373 712000 632346 250619 352601 841126 853040 933224 708521 > 3²⁴⁵ [i]