MinT - Best Known (247−85, 247, s)-Nets in Base 3

Best Known (247−85, 247, s)-Nets in Base 3

(247−85, 247, 162)-Net over F₃ — Constructive and digital

Digital (162, 247, 162)-net over F₃, using

t-expansion [i] based on digital (157, 247, 162)-net over F₃, using
- 3 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]

(247−85, 247, 347)-Net over F₃ — Digital

Digital (162, 247, 347)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−85, 247, 5103)-Net in Base 3 — Upper bound on s

There is no (162, 247, 5104)-net in base 3, because

1 times m-reduction [i] would yield (162, 246, 5104)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2371 629526 369218 973957 924884 348727 878469 384787 473560 919529 437604 169740 659514 079592 953830 452334 309023 947431 545400 562849 > 3²⁴⁶ [i]