MinT - Best Known (164−65, 164, s)-Nets in Base 3

Best Known (164−65, 164, s)-Nets in Base 3

(164−65, 164, 148)-Net over F₃ — Constructive and digital

Digital (99, 164, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 82, 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]

(164−65, 164, 162)-Net over F₃ — Digital

Digital (99, 164, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−65, 164, 1691)-Net in Base 3 — Upper bound on s

There is no (99, 164, 1692)-net in base 3, because

1 times m-reduction [i] would yield (99, 163, 1692)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 597075 052016 354965 141202 764141 592198 793122 293920 656181 296766 537355 661209 512193 > 3¹⁶³ [i]