MinT - Best Known (194−77, 194, s)-Nets in Base 3

Best Known (194−77, 194, s)-Nets in Base 3

(194−77, 194, 148)-Net over F₃ — Constructive and digital

Digital (117, 194, 148)-net over F₃, using

6 times m-reduction [i] based on digital (117, 200, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 100, 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]

(194−77, 194, 186)-Net over F₃ — Digital

Digital (117, 194, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−77, 194, 1953)-Net in Base 3 — Upper bound on s

There is no (117, 194, 1954)-net in base 3, because

1 times m-reduction [i] would yield (117, 193, 1954)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 122 194732 521315 719731 654681 363361 470995 283554 829850 797305 485175 444179 351184 373262 992622 776125 > 3¹⁹³ [i]