MinT - Best Known (109, 109+65, s)-Nets in Base 3

Best Known (109, 109+65, s)-Nets in Base 3

(109, 109+65, 156)-Net over F₃ — Constructive and digital

Digital (109, 174, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 87, 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]

(109, 109+65, 201)-Net over F₃ — Digital

Digital (109, 174, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+65, 2396)-Net in Base 3 — Upper bound on s

There is no (109, 174, 2397)-net in base 3, because

1 times m-reduction [i] would yield (109, 173, 2397)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34884 905402 807264 631741 627250 138604 811761 816337 360527 123300 915170 613170 086456 294273 > 3¹⁷³ [i]