MinT - Best Known (126, 126+99, s)-Nets in Base 3

Best Known (126, 126+99, s)-Nets in Base 3

(126, 126+99, 128)-Net over F₃ — Constructive and digital

Digital (126, 225, 128)-net over F₃, using

1 times m-reduction [i] based on digital (126, 226, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 113, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(126, 126+99, 159)-Net over F₃ — Digital

Digital (126, 225, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+99, 1402)-Net in Base 3 — Upper bound on s

There is no (126, 225, 1403)-net in base 3, because

1 times m-reduction [i] would yield (126, 224, 1403)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76852 974759 797341 157729 775762 721566 360759 484595 230345 614590 585119 331236 381493 343705 277330 271040 409498 250775 > 3²²⁴ [i]