MinT - Best Known (211−63, 211, s)-Nets in Base 4

Best Known (211−63, 211, s)-Nets in Base 4

(211−63, 211, 531)-Net over F₄ — Constructive and digital

Digital (148, 211, 531)-net over F₄, using

4¹ times duplication [i] based on digital (147, 210, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 70, 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]

(211−63, 211, 885)-Net over F₄ — Digital

Digital (148, 211, 885)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−63, 211, 49563)-Net in Base 4 — Upper bound on s

There is no (148, 211, 49564)-net in base 4, because

1 times m-reduction [i] would yield (148, 210, 49564)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 708770 061281 283428 846051 866127 694068 476383 235208 661022 895701 494864 281976 680876 304834 107519 511978 368415 775871 028495 561495 014240 > 4²¹⁰ [i]