MinT - Best Known (130−40, 130, s)-Nets in Base 16

Best Known (130−40, 130, s)-Nets in Base 16

(130−40, 130, 1038)-Net over F₁₆ — Constructive and digital

Digital (90, 130, 1038)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (24, 44, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 22, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (46, 86, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 43, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(130−40, 130, 10614)-Net over F₁₆ — Digital

Digital (90, 130, 10614)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−40, 130, large)-Net in Base 16 — Upper bound on s

There is no (90, 130, large)-net in base 16, because

38 times m-reduction [i] would yield (90, 92, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]