MinT - Best Known (51−15, 51, s)-Nets in Base 2

Best Known (51−15, 51, s)-Nets in Base 2

(51−15, 51, 59)-Net over F₂ — Constructive and digital

Digital (36, 51, 59)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 15, 23)-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]

(51−15, 51, 69)-Net over F₂ — Digital

Digital (36, 51, 69)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−15, 51, 467)-Net in Base 2 — Upper bound on s

There is no (36, 51, 468)-net in base 2, because

1 times m-reduction [i] would yield (36, 50, 468)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1129 756622 232460 > 2⁵⁰ [i]