MinT - Best Known (248−87, 248, s)-Nets in Base 3

Best Known (248−87, 248, s)-Nets in Base 3

(248−87, 248, 162)-Net over F₃ — Constructive and digital

Digital (161, 248, 162)-net over F₃, using

t-expansion [i] based on digital (157, 248, 162)-net over F₃, using
- 2 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]

(248−87, 248, 329)-Net over F₃ — Digital

Digital (161, 248, 329)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−87, 248, 4604)-Net in Base 3 — Upper bound on s

There is no (161, 248, 4605)-net in base 3, because

1 times m-reduction [i] would yield (161, 247, 4605)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7127 357325 103316 873427 762404 325998 235155 503072 847211 517656 822200 370182 000683 702028 965116 003926 063708 662972 539985 887147 > 3²⁴⁷ [i]