MinT - Best Known (216−65, 216, s)-Nets in Base 4

Best Known (216−65, 216, s)-Nets in Base 4

(216−65, 216, 531)-Net over F₄ — Constructive and digital

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]

(216−65, 216, 874)-Net over F₄ — Digital

Digital (151, 216, 874)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−65, 216, 47272)-Net in Base 4 — Upper bound on s

There is no (151, 216, 47273)-net in base 4, because

1 times m-reduction [i] would yield (151, 215, 47273)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2773 437774 163583 779714 737013 016418 974661 872691 440432 567312 108591 264457 667772 184458 577643 895052 229506 954928 158126 403221 763385 671657 > 4²¹⁵ [i]