MinT - Best Known (106−34, 106, s)-Nets in Base 16

Best Known (106−34, 106, s)-Nets in Base 16

(106−34, 106, 1032)-Net over F₁₆ — Constructive and digital

Digital (72, 106, 1032)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (19, 36, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 18, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (36, 70, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 35, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(106−34, 106, 6488)-Net over F₁₆ — Digital

Digital (72, 106, 6488)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−34, 106, large)-Net in Base 16 — Upper bound on s

There is no (72, 106, large)-net in base 16, because

32 times m-reduction [i] would yield (72, 74, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]