MinT - Best Known (159−56, 159, s)-Nets in Base 3

Best Known (159−56, 159, s)-Nets in Base 3

(159−56, 159, 156)-Net over F₃ — Constructive and digital

Digital (103, 159, 156)-net over F₃, using

3 times m-reduction [i] based on digital (103, 162, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 81, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(159−56, 159, 222)-Net over F₃ — Digital

Digital (103, 159, 222)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−56, 159, 2865)-Net in Base 3 — Upper bound on s

There is no (103, 159, 2866)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7313 073745 192389 801685 420248 183857 372764 994754 890361 018060 605524 548780 860697 > 3¹⁵⁹ [i]