MinT - Best Known (126, 126+53, s)-Nets in Base 4

Best Known (126, 126+53, s)-Nets in Base 4

(126, 126+53, 384)-Net over F₄ — Constructive and digital

Digital (126, 179, 384)-net over F₄, using

t-expansion [i] based on digital (125, 179, 384)-net over F₄, using
- 1 times m-reduction [i] based on digital (125, 180, 384)-net over F₄, using
  - trace code for nets [i] based on digital (5, 60, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(126, 126+53, 799)-Net over F₄ — Digital

Digital (126, 179, 799)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+53, 46533)-Net in Base 4 — Upper bound on s

There is no (126, 179, 46534)-net in base 4, because

1 times m-reduction [i] would yield (126, 178, 46534)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 146790 424585 372794 275482 347098 953675 439360 487186 918509 220666 335303 870729 846989 281381 965179 285292 557129 830256 > 4¹⁷⁸ [i]