MinT - Best Known (105−33, 105, s)-Nets in Base 3

Best Known (105−33, 105, s)-Nets in Base 3

(105−33, 105, 148)-Net over F₃ — Constructive and digital

Digital (72, 105, 148)-net over F₃, using

5 times m-reduction [i] based on digital (72, 110, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 55, 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]

(105−33, 105, 225)-Net over F₃ — Digital

Digital (72, 105, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−33, 105, 4277)-Net in Base 3 — Upper bound on s

There is no (72, 105, 4278)-net in base 3, because

1 times m-reduction [i] would yield (72, 104, 4278)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41 764371 999436 004360 148394 442525 688989 703370 191009 > 3¹⁰⁴ [i]