MinT - Best Known (25, 39, s)-Nets in Base 4

Best Known (25, 39, s)-Nets in Base 4

(25, 39, 98)-Net over F₄ — Constructive and digital

Digital (25, 39, 98)-net over F₄, using

1 times m-reduction [i] based on digital (25, 40, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 20, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(25, 39, 128)-Net over F₄ — Digital

Digital (25, 39, 128)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4³⁹, 128, F₄, 14) (dual of [128, 89, 15]-code), using
- a â€œGraâ€ code from Grasslâ€™s database [i]

(25, 39, 2542)-Net in Base 4 — Upper bound on s

There is no (25, 39, 2543)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 302835 365337 274908 251884 > 4³⁹ [i]