MinT - Best Known (170−46, 170, s)-Nets in Base 4

Best Known (170−46, 170, s)-Nets in Base 4

(170−46, 170, 531)-Net over F₄ — Constructive and digital

Digital (124, 170, 531)-net over F₄, using

t-expansion [i] based on digital (123, 170, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (123, 174, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 58, 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]

(170−46, 170, 1128)-Net over F₄ — Digital

Digital (124, 170, 1128)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−46, 170, 88562)-Net in Base 4 — Upper bound on s

There is no (124, 170, 88563)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 239766 510159 160397 492303 045095 844422 167783 959900 333219 921781 985909 641747 208519 873452 029860 575653 380160 > 4¹⁷⁰ [i]