MinT - Best Known (87, 87+39, s)-Nets in Base 16

Best Known (87, 87+39, s)-Nets in Base 16

(87, 87+39, 1038)-Net over F₁₆ — Constructive and digital

Digital (87, 126, 1038)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (23, 42, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 21, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-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, using
      - Niederreiter sequence [i]

(87, 87+39, 9866)-Net over F₁₆ — Digital

Digital (87, 126, 9866)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+39, large)-Net in Base 16 — Upper bound on s

There is no (87, 126, large)-net in base 16, because

37 times m-reduction [i] would yield (87, 89, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]