MinT - Best Known (194−80, 194, s)-Nets in Base 3

Best Known (194−80, 194, s)-Nets in Base 3

(194−80, 194, 148)-Net over F₃ — Constructive and digital

Digital (114, 194, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 97, 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]

(194−80, 194, 167)-Net over F₃ — Digital

Digital (114, 194, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−80, 194, 1585)-Net in Base 3 — Upper bound on s

There is no (114, 194, 1586)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 367 118732 266695 064990 995686 958146 818326 629074 703928 704211 413056 597835 151539 494418 636826 988689 > 3¹⁹⁴ [i]