MinT - Best Known (91−41, 91, s)-Nets in Base 4

Best Known (91−41, 91, s)-Nets in Base 4

(91−41, 91, 90)-Net over F₄ — Constructive and digital

Digital (50, 91, 90)-net over F₄, using

1 times m-reduction [i] based on digital (50, 92, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 46, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(91−41, 91, 103)-Net over F₄ — Digital

Digital (50, 91, 103)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−41, 91, 1401)-Net in Base 4 — Upper bound on s

There is no (50, 91, 1402)-net in base 4, because

1 times m-reduction [i] would yield (50, 90, 1402)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 550286 483137 446740 966636 665380 754677 329940 052025 881446 > 4⁹⁰ [i]