MinT - Best Known (216−73, 216, s)-Nets in Base 3

Best Known (216−73, 216, s)-Nets in Base 3

(216−73, 216, 162)-Net over F₃ — Constructive and digital

Digital (143, 216, 162)-net over F₃, using

6 times m-reduction [i] based on digital (143, 222, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 111, 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]

(216−73, 216, 326)-Net over F₃ — Digital

Digital (143, 216, 326)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−73, 216, 5013)-Net in Base 3 — Upper bound on s

There is no (143, 216, 5014)-net in base 3, because

1 times m-reduction [i] would yield (143, 215, 5014)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 829699 663170 871126 777610 618646 199489 882510 523843 794082 243110 373294 455605 204852 094611 618238 078327 877449 > 3²¹⁵ [i]