MinT - Best Known (164−46, 164, s)-Nets in Base 4

Best Known (164−46, 164, s)-Nets in Base 4

(164−46, 164, 531)-Net over F₄ — Constructive and digital

Digital (118, 164, 531)-net over F₄, using

t-expansion [i] based on digital (117, 164, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (117, 165, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 55, 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]

(164−46, 164, 941)-Net over F₄ — Digital

Digital (118, 164, 941)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−46, 164, 61681)-Net in Base 4 — Upper bound on s

There is no (118, 164, 61682)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 546 966562 995052 325594 860935 819575 248198 770535 515161 577170 598057 888811 472050 650884 237277 388842 167632 > 4¹⁶⁴ [i]