MinT - Best Known (223−75, 223, s)-Nets in Base 3

Best Known (223−75, 223, s)-Nets in Base 3

(223−75, 223, 162)-Net over F₃ — Constructive and digital

Digital (148, 223, 162)-net over F₃, using

9 times m-reduction [i] based on digital (148, 232, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 116, 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]

(223−75, 223, 340)-Net over F₃ — Digital

Digital (148, 223, 340)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−75, 223, 5304)-Net in Base 3 — Upper bound on s

There is no (148, 223, 5305)-net in base 3, because

1 times m-reduction [i] would yield (148, 222, 5305)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8367 589579 857501 606858 443101 113849 883986 941484 959642 938580 373050 564223 454758 531134 920098 978679 959790 673763 > 3²²² [i]