MinT - Best Known (215−63, 215, s)-Nets in Base 4

Best Known (215−63, 215, s)-Nets in Base 4

(215−63, 215, 531)-Net over F₄ — Constructive and digital

Digital (152, 215, 531)-net over F₄, using

t-expansion [i] based on digital (151, 215, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 72, 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]

(215−63, 215, 973)-Net over F₄ — Digital

Digital (152, 215, 973)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−63, 215, 59276)-Net in Base 4 — Upper bound on s

There is no (152, 215, 59277)-net in base 4, because

1 times m-reduction [i] would yield (152, 214, 59277)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 364199 298184 490767 488391 147403 458705 642794 635503 719544 411938 660134 348242 418628 722803 732059 347348 074623 094473 435120 231712 583296 > 4²¹⁴ [i]