MinT - Best Known (104, 174, s)-Nets in Base 3

Best Known (104, 174, s)-Nets in Base 3

(104, 174, 148)-Net over F₃ — Constructive and digital

Digital (104, 174, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 87, 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]

(104, 174, 163)-Net over F₃ — Digital

Digital (104, 174, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 174, 1603)-Net in Base 3 — Upper bound on s

There is no (104, 174, 1604)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 105842 459124 997665 857159 538820 950641 121209 692575 007332 039293 675105 025974 489050 960689 > 3¹⁷⁴ [i]