MinT - Best Known (88−28, 88, s)-Nets in Base 16

Best Known (88−28, 88, s)-Nets in Base 16

(88−28, 88, 1032)-Net over F₁₆ — Constructive and digital

Digital (60, 88, 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 (30, 58, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 29, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(88−28, 88, 6135)-Net over F₁₆ — Digital

Digital (60, 88, 6135)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−28, 88, large)-Net in Base 16 — Upper bound on s

There is no (60, 88, large)-net in base 16, because

26 times m-reduction [i] would yield (60, 62, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]