MinT - Best Known (23, 23+11, s)-Nets in Base 2

Best Known (23, 23+11, s)-Nets in Base 2

(23, 23+11, 46)-Net over F₂ — Constructive and digital

Digital (23, 34, 46)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 11, 26)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (12, 23, 23)-net over F₂, using
  - a shift-net [i]

(23, 23+11, 245)-Net in Base 2 — Upper bound on s

There is no (23, 34, 246)-net in base 2, because

1 times m-reduction [i] would yield (23, 33, 246)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 8624 154431 > 2³³ [i]