MinT - Best Known (28, 28+19, s)-Nets in Base 4

Best Known (28, 28+19, s)-Nets in Base 4

(28, 28+19, 90)-Net over F₄ — Constructive and digital

Digital (28, 47, 90)-net over F₄, using

1 times m-reduction [i] based on digital (28, 48, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 24, 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]

(28, 28+19, 92)-Net over F₄ — Digital

Digital (28, 47, 92)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 28+19, 1644)-Net in Base 4 — Upper bound on s

There is no (28, 47, 1645)-net in base 4, because

1 times m-reduction [i] would yield (28, 46, 1645)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4970 396222 427315 875696 277328 > 4⁴⁶ [i]