MinT - Best Known (88, 88+40, s)-Nets in Base 16

Best Known (88, 88+40, s)-Nets in Base 16

(88, 88+40, 1036)-Net over F₁₆ — Constructive and digital

Digital (88, 128, 1036)-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 (44, 84, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 42, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(88, 88+40, 9209)-Net over F₁₆ — Digital

Digital (88, 128, 9209)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+40, large)-Net in Base 16 — Upper bound on s

There is no (88, 128, large)-net in base 16, because

38 times m-reduction [i] would yield (88, 90, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]