MinT - Best Known (90−29, 90, s)-Nets in Base 16

Best Known (90−29, 90, s)-Nets in Base 16

(90−29, 90, 1032)-Net over F₁₆ — Constructive and digital

Digital (61, 90, 1032)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (16, 30, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 15, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (31, 60, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 30, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(90−29, 90, 5602)-Net over F₁₆ — Digital

Digital (61, 90, 5602)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−29, 90, large)-Net in Base 16 — Upper bound on s

There is no (61, 90, large)-net in base 16, because

27 times m-reduction [i] would yield (61, 63, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]