MinT - Best Known (111, 178, s)-Nets in Base 3

Best Known (111, 178, s)-Nets in Base 3

(111, 178, 156)-Net over F₃ — Constructive and digital

Digital (111, 178, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 89, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(111, 178, 201)-Net over F₃ — Digital

Digital (111, 178, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 178, 2352)-Net in Base 3 — Upper bound on s

There is no (111, 178, 2353)-net in base 3, because

1 times m-reduction [i] would yield (111, 177, 2353)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 846570 658141 058135 170384 656830 580885 741517 939655 651017 732519 176045 284195 018125 373923 > 3¹⁷⁷ [i]