MinT - Best Known (52−15, 52, s)-Nets in Base 2

Best Known (52−15, 52, s)-Nets in Base 2

(52−15, 52, 64)-Net over F₂ — Constructive and digital

Digital (37, 52, 64)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 16, 28)-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]

(52−15, 52, 73)-Net over F₂ — Digital

Digital (37, 52, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−15, 52, 517)-Net in Base 2 — Upper bound on s

There is no (37, 52, 518)-net in base 2, because

1 times m-reduction [i] would yield (37, 51, 518)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2267 416380 868140 > 2⁵¹ [i]