MinT - Best Known (124, 124+39, s)-Nets in Base 3

Best Known (124, 124+39, s)-Nets in Base 3

(124, 124+39, 400)-Net over F₃ — Constructive and digital

Digital (124, 163, 400)-net over F₃, using

1 times m-reduction [i] based on digital (124, 164, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 41, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(124, 124+39, 855)-Net over F₃ — Digital

Digital (124, 163, 855)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+39, 46355)-Net in Base 3 — Upper bound on s

There is no (124, 163, 46356)-net in base 3, because

1 times m-reduction [i] would yield (124, 162, 46356)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196689 107766 838211 359468 460430 512798 291690 693387 537897 556859 902013 163304 599281 > 3¹⁶² [i]