MinT - Best Known (31−11, 31, s)-Nets in Base 2

Best Known (31−11, 31, s)-Nets in Base 2

(31−11, 31, 36)-Net over F₂ — Constructive and digital

Digital (20, 31, 36)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 10, 20)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (10, 21, 18)-net over F₂, using
  - linear code embedding found in a computer search [i]

(31−11, 31, 159)-Net in Base 2 — Upper bound on s

There is no (20, 31, 160)-net in base 2, because

1 times m-reduction [i] would yield (20, 30, 160)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1078 429033 > 2³⁰ [i]