MinT - Best Known (144, 144+73, s)-Nets in Base 3

Best Known (144, 144+73, s)-Nets in Base 3

(144, 144+73, 162)-Net over F₃ — Constructive and digital

Digital (144, 217, 162)-net over F₃, using

7 times m-reduction [i] based on digital (144, 224, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 112, 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]

(144, 144+73, 332)-Net over F₃ — Digital

Digital (144, 217, 332)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+73, 5169)-Net in Base 3 — Upper bound on s

There is no (144, 217, 5170)-net in base 3, because

1 times m-reduction [i] would yield (144, 216, 5170)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 452237 284240 793618 604999 388384 809808 040188 223449 265192 350718 736465 731352 581233 748097 410176 424756 252265 > 3²¹⁶ [i]