MinT - Best Known (72−22, 72, s)-Nets in Base 16

Best Known (72−22, 72, s)-Nets in Base 16

(72−22, 72, 1034)-Net over F₁₆ — Constructive and digital

Digital (50, 72, 1034)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (13, 24, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 12, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (26, 48, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 24, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(72−22, 72, 7787)-Net over F₁₆ — Digital

Digital (50, 72, 7787)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−22, 72, large)-Net in Base 16 — Upper bound on s

There is no (50, 72, large)-net in base 16, because

20 times m-reduction [i] would yield (50, 52, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]