MinT - Best Known (124, 124+87, s)-Nets in Base 3

Best Known (124, 124+87, s)-Nets in Base 3

(124, 124+87, 148)-Net over F₃ — Constructive and digital

Digital (124, 211, 148)-net over F₃, using

3 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+87, 180)-Net over F₃ — Digital

Digital (124, 211, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+87, 1763)-Net in Base 3 — Upper bound on s

There is no (124, 211, 1764)-net in base 3, because

1 times m-reduction [i] would yield (124, 210, 1764)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15955 684330 530154 743586 992145 951058 093168 189033 215758 864380 718548 502173 333277 767286 887150 527569 770865 > 3²¹⁰ [i]