MinT - Best Known (128, 128+37, s)-Nets in Base 3

Best Known (128, 128+37, s)-Nets in Base 3

(128, 128+37, 600)-Net over F₃ — Constructive and digital

Digital (128, 165, 600)-net over F₃, using

3¹ times duplication [i] based on digital (127, 164, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 41, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(128, 128+37, 1115)-Net over F₃ — Digital

Digital (128, 165, 1115)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+37, 83968)-Net in Base 3 — Upper bound on s

There is no (128, 165, 83969)-net in base 3, because

1 times m-reduction [i] would yield (128, 164, 83969)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 769984 470129 225313 893814 913368 042778 401351 000064 194527 434352 392080 886717 833545 > 3¹⁶⁴ [i]