MinT - Best Known (133, 133+99, s)-Nets in Base 3

Best Known (133, 133+99, s)-Nets in Base 3

(133, 133+99, 148)-Net over F₃ — Constructive and digital

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+99, 178)-Net over F₃ — Digital

Digital (133, 232, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+99, 1648)-Net in Base 3 — Upper bound on s

There is no (133, 232, 1649)-net in base 3, because

1 times m-reduction [i] would yield (133, 231, 1649)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 165 922551 656621 226743 696810 165746 544213 041156 057070 900391 771246 293119 756348 713095 627865 457046 866292 562408 469539 > 3²³¹ [i]