MinT - Best Known (136, 136+55, s)-Nets in Base 4

Best Known (136, 136+55, s)-Nets in Base 4

(136, 136+55, 531)-Net over F₄ — Constructive and digital

Digital (136, 191, 531)-net over F₄, using

t-expansion [i] based on digital (135, 191, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(136, 136+55, 950)-Net over F₄ — Digital

Digital (136, 191, 950)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+55, 62784)-Net in Base 4 — Upper bound on s

There is no (136, 191, 62785)-net in base 4, because

1 times m-reduction [i] would yield (136, 190, 62785)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 463246 495028 023501 173295 252242 535157 147597 761971 048562 176105 042396 013116 988582 052466 242066 350005 375587 887378 757312 > 4¹⁹⁰ [i]