MinT - Best Known (133, 133+67, s)-Nets in Base 3

Best Known (133, 133+67, s)-Nets in Base 3

(133, 133+67, 162)-Net over F₃ — Constructive and digital

Digital (133, 200, 162)-net over F₃, using

2 times m-reduction [i] based on digital (133, 202, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 101, 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]

(133, 133+67, 313)-Net over F₃ — Digital

Digital (133, 200, 313)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+67, 4927)-Net in Base 3 — Upper bound on s

There is no (133, 200, 4928)-net in base 3, because

1 times m-reduction [i] would yield (133, 199, 4928)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88590 683217 752849 830423 296818 386322 240400 155918 194975 158043 864806 092815 835852 458397 415530 583681 > 3¹⁹⁹ [i]