MinT - Best Known (101, 101+45, s)-Nets in Base 4

Best Known (101, 101+45, s)-Nets in Base 4

(101, 101+45, 312)-Net over F₄ — Constructive and digital

Digital (101, 146, 312)-net over F₄, using

1 times m-reduction [i] based on digital (101, 147, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 49, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(101, 101+45, 573)-Net over F₄ — Digital

Digital (101, 146, 573)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+45, 28027)-Net in Base 4 — Upper bound on s

There is no (101, 146, 28028)-net in base 4, because

1 times m-reduction [i] would yield (101, 145, 28028)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1990 687983 627376 403796 885058 562916 694983 779183 595018 951381 172011 819621 895794 315779 771638 > 4¹⁴⁵ [i]