MinT - Best Known (178−52, 178, s)-Nets in Base 4

Best Known (178−52, 178, s)-Nets in Base 4

(178−52, 178, 531)-Net over F₄ — Constructive and digital

Digital (126, 178, 531)-net over F₄, using

4¹ times duplication [i] based on digital (125, 177, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 59, 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]

(178−52, 178, 843)-Net over F₄ — Digital

Digital (126, 178, 843)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−52, 178, 46533)-Net in Base 4 — Upper bound on s

There is no (126, 178, 46534)-net in base 4, because

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]