MinT - Best Known (28, 28+13, s)-Nets in Base 2

Best Known (28, 28+13, s)-Nets in Base 2

(28, 28+13, 50)-Net over F₂ — Constructive and digital

Digital (28, 41, 50)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 12, 21)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (16, 29, 29)-net over F₂, using
  - a shift-net [i]

(28, 28+13, 51)-Net over F₂ — Digital

Digital (28, 41, 51)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 28+13, 295)-Net in Base 2 — Upper bound on s

There is no (28, 41, 296)-net in base 2, because

1 times m-reduction [i] would yield (28, 40, 296)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 104886 406047 > 2⁴⁰ [i]