MinT - Best Known (22, 35, s)-Nets in Base 4

Best Known (22, 35, s)-Nets in Base 4

(22, 35, 90)-Net over F₄ — Constructive and digital

Digital (22, 35, 90)-net over F₄, using

1 times m-reduction [i] based on digital (22, 36, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 18, 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]

(22, 35, 112)-Net over F₄ — Digital

Digital (22, 35, 112)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4³⁵, 112, F₄, 13) (dual of [112, 77, 14]-code), using
- a code from Grasslâ€™s database [i]

(22, 35, 2570)-Net in Base 4 — Upper bound on s

There is no (22, 35, 2571)-net in base 4, because

1 times m-reduction [i] would yield (22, 34, 2571)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 295 502505 579756 222274 > 4³⁴ [i]