MinT - Best Known (27, 39, s)-Nets in Base 2

Best Known (27, 39, s)-Nets in Base 2

(27, 39, 50)-Net over F₂ — Constructive and digital

Digital (27, 39, 50)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 14, 26)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (13, 25, 25)-net over F₂, using
  - a shift-net [i]

(27, 39, 53)-Net over F₂ — Digital

Digital (27, 39, 53)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 39, 262)-Net in Base 2 — Upper bound on s

There is no (27, 39, 263)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 554867 200861 > 2³⁹ [i]