MinT - Best Known (101, 101+67, s)-Nets in Base 3

Best Known (101, 101+67, s)-Nets in Base 3

(101, 101+67, 148)-Net over F₃ — Constructive and digital

Digital (101, 168, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 84, 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]

(101, 101+67, 162)-Net over F₃ — Digital

Digital (101, 168, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+67, 1677)-Net in Base 3 — Upper bound on s

There is no (101, 168, 1678)-net in base 3, because

1 times m-reduction [i] would yield (101, 167, 1678)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48 554163 954294 120065 708049 121331 361143 534725 389508 965865 438935 897422 771012 500701 > 3¹⁶⁷ [i]