MinT - Best Known (44−25, 44, s)-Nets in Base 256

Best Known (44−25, 44, s)-Nets in Base 256

(44−25, 44, 521)-Net over F₂₅₆ — Constructive and digital

Digital (19, 44, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 15, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 29, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(44−25, 44, 1012)-Net over F₂₅₆ — Digital

Digital (19, 44, 1012)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−25, 44, large)-Net in Base 256 — Upper bound on s

There is no (19, 44, large)-net in base 256, because

23 times m-reduction [i] would yield (19, 21, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]