MinT - Best Known (106, 106+65, s)-Nets in Base 3

Best Known (106, 106+65, s)-Nets in Base 3

(106, 106+65, 148)-Net over F₃ — Constructive and digital

Digital (106, 171, 148)-net over F₃, using

7 times m-reduction [i] based on digital (106, 178, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 89, 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]

(106, 106+65, 189)-Net over F₃ — Digital

Digital (106, 171, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+65, 2159)-Net in Base 3 — Upper bound on s

There is no (106, 171, 2160)-net in base 3, because

1 times m-reduction [i] would yield (106, 170, 2160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1304 142523 440003 772063 979367 397369 302104 036347 227078 929849 479745 446569 252655 212545 > 3¹⁷⁰ [i]