MinT - Best Known (160, 160+89, s)-Nets in Base 3

Best Known (160, 160+89, s)-Nets in Base 3

(160, 160+89, 162)-Net over F₃ — Constructive and digital

Digital (160, 249, 162)-net over F₃, using

t-expansion [i] based on digital (157, 249, 162)-net over F₃, using
- 1 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]

(160, 160+89, 313)-Net over F₃ — Digital

Digital (160, 249, 313)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+89, 4174)-Net in Base 3 — Upper bound on s

There is no (160, 249, 4175)-net in base 3, because

1 times m-reduction [i] would yield (160, 248, 4175)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21224 200133 948546 781702 574240 690900 453510 943247 762080 530467 888193 751148 601015 317370 037426 501952 630195 973285 699361 363625 > 3²⁴⁸ [i]