MinT - Best Known (109, 109+107, s)-Nets in Base 3

Best Known (109, 109+107, s)-Nets in Base 3

(109, 109+107, 74)-Net over F₃ — Constructive and digital

Digital (109, 216, 74)-net over F₃, using

t-expansion [i] based on digital (107, 216, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [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]

(109, 109+107, 110)-Net over F₃ — Digital

Digital (109, 216, 110)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+107, 836)-Net in Base 3 — Upper bound on s

There is no (109, 216, 837)-net in base 3, because

1 times m-reduction [i] would yield (109, 215, 837)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 944119 125898 761701 788749 610153 252395 901192 999771 028124 757907 625295 333506 839278 097602 422352 223451 326427 > 3²¹⁵ [i]