MinT - Best Known (123−47, 123, s)-Nets in Base 3

Best Known (123−47, 123, s)-Nets in Base 3

(123−47, 123, 128)-Net over F₃ — Constructive and digital

Digital (76, 123, 128)-net over F₃, using

3 times m-reduction [i] based on digital (76, 126, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 63, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(123−47, 123, 141)-Net over F₃ — Digital

Digital (76, 123, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−47, 123, 1578)-Net in Base 3 — Upper bound on s

There is no (76, 123, 1579)-net in base 3, because

1 times m-reduction [i] would yield (76, 122, 1579)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16386 898478 757858 757539 848818 468482 849253 564469 462929 108995 > 3¹²² [i]