MinT - Best Known (214−71, 214, s)-Nets in Base 3

Best Known (214−71, 214, s)-Nets in Base 3

(214−71, 214, 162)-Net over F₃ — Constructive and digital

Digital (143, 214, 162)-net over F₃, using

8 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]

(214−71, 214, 342)-Net over F₃ — Digital

Digital (143, 214, 342)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−71, 214, 5535)-Net in Base 3 — Upper bound on s

There is no (143, 214, 5536)-net in base 3, because

1 times m-reduction [i] would yield (143, 213, 5536)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 424493 186296 853853 179284 461618 988859 557951 285044 645175 308350 660784 547066 023653 193474 311645 375678 347905 > 3²¹³ [i]