MinT - Best Known (217−65, 217, s)-Nets in Base 4

Best Known (217−65, 217, s)-Nets in Base 4

(217−65, 217, 531)-Net over F₄ — Constructive and digital

Digital (152, 217, 531)-net over F₄, using

4¹ times duplication [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]

(217−65, 217, 895)-Net over F₄ — Digital

Digital (152, 217, 895)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−65, 217, 49366)-Net in Base 4 — Upper bound on s

There is no (152, 217, 49367)-net in base 4, because

1 times m-reduction [i] would yield (152, 216, 49367)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11092 942332 391512 124066 038982 245668 847961 582816 040841 142784 208921 351929 514739 783154 089075 522656 356547 801137 488222 671158 150697 649750 > 4²¹⁶ [i]