MinT - Best Known (42−13, 42, s)-Nets in Base 2

Best Known (42−13, 42, s)-Nets in Base 2

(42−13, 42, 52)-Net over F₂ — Constructive and digital

Digital (29, 42, 52)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 13, 23)-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]

(42−13, 42, 54)-Net over F₂ — Digital

Digital (29, 42, 54)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(42−13, 42, 332)-Net in Base 2 — Upper bound on s

There is no (29, 42, 333)-net in base 2, because

1 times m-reduction [i] would yield (29, 41, 333)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 199461 190592 > 2⁴¹ [i]