MinT - Best Known (214−64, 214, s)-Nets in Base 4

Best Known (214−64, 214, s)-Nets in Base 4

(214−64, 214, 531)-Net over F₄ — Constructive and digital

Digital (150, 214, 531)-net over F₄, using

4¹ times duplication [i] based on digital (149, 213, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 71, 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]

(214−64, 214, 890)-Net over F₄ — Digital

Digital (150, 214, 890)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−64, 214, 45267)-Net in Base 4 — Upper bound on s

There is no (150, 214, 45268)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 520629 831939 703787 574452 218198 051707 856436 885398 955506 411049 690128 336171 502132 811320 202379 686922 037680 221632 490431 325328 226566 > 4²¹⁴ [i]