MinT - Best Known (89, 89+39, s)-Nets in Base 16

Best Known (89, 89+39, s)-Nets in Base 16

(89, 89+39, 1040)-Net over F₁₆ — Constructive and digital

Digital (89, 128, 1040)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (25, 44, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 22, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (45, 84, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 42, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆ (see above)

(89, 89+39, 11413)-Net over F₁₆ — Digital

Digital (89, 128, 11413)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+39, large)-Net in Base 16 — Upper bound on s

There is no (89, 128, large)-net in base 16, because

37 times m-reduction [i] would yield (89, 91, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]