MinT - Best Known (105, 176, s)-Nets in Base 3

Best Known (105, 176, s)-Nets in Base 3

(105, 176, 148)-Net over F₃ — Constructive and digital

Digital (105, 176, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 88, 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]

(105, 176, 163)-Net over F₃ — Digital

Digital (105, 176, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 176, 1655)-Net in Base 3 — Upper bound on s

There is no (105, 176, 1656)-net in base 3, because

1 times m-reduction [i] would yield (105, 175, 1656)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 316033 500023 484849 418016 685044 640064 924246 710900 544625 614590 897400 767666 871006 682465 > 3¹⁷⁵ [i]