MinT - Best Known (124, 124+41, s)-Nets in Base 3

Best Known (124, 124+41, s)-Nets in Base 3

(124, 124+41, 328)-Net over F₃ — Constructive and digital

Digital (124, 165, 328)-net over F₃, using

3¹ times duplication [i] based on digital (123, 164, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 41, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(124, 124+41, 747)-Net over F₃ — Digital

Digital (124, 165, 747)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+41, 33917)-Net in Base 3 — Upper bound on s

There is no (124, 165, 33918)-net in base 3, because

1 times m-reduction [i] would yield (124, 164, 33918)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 770398 509992 701018 650020 575756 201130 020884 507449 285324 197662 219267 908845 832873 > 3¹⁶⁴ [i]