MinT - Best Known (109, 109+112, s)-Nets in Base 3

Best Known (109, 109+112, s)-Nets in Base 3

(109, 109+112, 74)-Net over F₃ — Constructive and digital

Digital (109, 221, 74)-net over F₃, using

t-expansion [i] based on digital (107, 221, 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+112, 105)-Net over F₃ — Digital

Digital (109, 221, 105)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+112, 774)-Net in Base 3 — Upper bound on s

There is no (109, 221, 775)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2786 373925 918929 547043 659254 332239 293331 367058 999393 279501 661815 442940 363469 212053 117196 096267 780461 000209 > 3²²¹ [i]