MinT - Best Known (216−59, 216, s)-Nets in Base 4

Best Known (216−59, 216, s)-Nets in Base 4

(216−59, 216, 531)-Net over F₄ — Constructive and digital

Digital (157, 216, 531)-net over F₄, using

9 times m-reduction [i] based on digital (157, 225, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 75, 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]

(216−59, 216, 1331)-Net over F₄ — Digital

Digital (157, 216, 1331)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−59, 216, 113098)-Net in Base 4 — Upper bound on s

There is no (157, 216, 113099)-net in base 4, because

1 times m-reduction [i] would yield (157, 215, 113099)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2772 788532 626284 650465 383277 623226 517239 929386 658659 405426 832273 373046 752256 388967 953635 097300 610774 058555 025676 604268 434131 774112 > 4²¹⁵ [i]