MinT - Best Known (153, 215, s)-Nets in Base 4

Best Known (153, 215, s)-Nets in Base 4

(153, 215, 531)-Net over F₄ — Constructive and digital

Digital (153, 215, 531)-net over F₄, using

4 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 73, 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]

(153, 215, 1042)-Net over F₄ — Digital

Digital (153, 215, 1042)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 215, 61988)-Net in Base 4 — Upper bound on s

There is no (153, 215, 61989)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2773 260862 468573 505650 716119 034145 405761 544769 571235 956768 181963 593302 934696 137873 135724 483521 790340 682517 066282 524713 628826 466720 > 4²¹⁵ [i]