MinT - Best Known (123−41, 123, s)-Nets in Base 3

Best Known (123−41, 123, s)-Nets in Base 3

(123−41, 123, 148)-Net over F₃ — Constructive and digital

Digital (82, 123, 148)-net over F₃, using

7 times m-reduction [i] based on digital (82, 130, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 65, 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]

(123−41, 123, 212)-Net over F₃ — Digital

Digital (82, 123, 212)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−41, 123, 3358)-Net in Base 3 — Upper bound on s

There is no (82, 123, 3359)-net in base 3, because

1 times m-reduction [i] would yield (82, 122, 3359)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16174 581521 047883 572427 654317 064343 849997 514190 968362 500057 > 3¹²² [i]