MinT - Best Known (49−15, 49, s)-Nets in Base 2

Best Known (49−15, 49, s)-Nets in Base 2

(49−15, 49, 52)-Net over F₂ — Constructive and digital

Digital (34, 49, 52)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 13, 16)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (21, 36, 36)-net over F₂, using
  - a shift-net [i]

(49−15, 49, 61)-Net over F₂ — Digital

Digital (34, 49, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−15, 49, 381)-Net in Base 2 — Upper bound on s

There is no (34, 49, 382)-net in base 2, because

1 times m-reduction [i] would yield (34, 48, 382)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 281 651121 198664 > 2⁴⁸ [i]