MinT - Best Known (55, 55+25, s)-Nets in Base 16

Best Known (55, 55+25, s)-Nets in Base 16

(55, 55+25, 1034)-Net over F₁₆ — Constructive and digital

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]

(55, 55+25, 6757)-Net over F₁₆ — Digital

Digital (55, 80, 6757)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+25, large)-Net in Base 16 — Upper bound on s

There is no (55, 80, large)-net in base 16, because

23 times m-reduction [i] would yield (55, 57, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]