MinT - Best Known (56, 56+25, s)-Nets in Base 16

Best Known (56, 56+25, s)-Nets in Base 16

(56, 56+25, 1034)-Net over F₁₆ — Constructive and digital

Digital (56, 81, 1034)-net over F₁₆, using

16¹ times duplication [i] based on digital (55, 80, 1034)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 26, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 13, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (29, 54, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 27, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(56, 56+25, 7583)-Net over F₁₆ — Digital

Digital (56, 81, 7583)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+25, large)-Net in Base 16 — Upper bound on s

There is no (56, 81, large)-net in base 16, because

23 times m-reduction [i] would yield (56, 58, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]