MinT - Best Known (133, 133+97, s)-Nets in Base 3

Best Known (133, 133+97, s)-Nets in Base 3

(133, 133+97, 148)-Net over F₃ — Constructive and digital

Digital (133, 230, 148)-net over F₃, using

2 times m-reduction [i] based on digital (133, 232, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 116, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(133, 133+97, 182)-Net over F₃ — Digital

Digital (133, 230, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+97, 1723)-Net in Base 3 — Upper bound on s

There is no (133, 230, 1724)-net in base 3, because

1 times m-reduction [i] would yield (133, 229, 1724)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 609789 541961 228223 663410 629431 868437 020150 270072 276964 741144 004084 596372 825815 331731 326279 811385 859378 050945 > 3²²⁹ [i]