MinT - Best Known (124, 124+85, s)-Nets in Base 3

Best Known (124, 124+85, s)-Nets in Base 3

(124, 124+85, 148)-Net over F₃ — Constructive and digital

Digital (124, 209, 148)-net over F₃, using

5 times m-reduction [i] based on digital (124, 214, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 107, 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]

(124, 124+85, 185)-Net over F₃ — Digital

Digital (124, 209, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+85, 1862)-Net in Base 3 — Upper bound on s

There is no (124, 209, 1863)-net in base 3, because

1 times m-reduction [i] would yield (124, 208, 1863)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1749 078473 555829 521726 486892 926401 807123 082279 206869 254781 274852 476627 372629 235318 657655 367838 546877 > 3²⁰⁸ [i]