MinT - Best Known (26, 26+10, s)-Nets in Base 2

Best Known (26, 26+10, s)-Nets in Base 2

(26, 26+10, 53)-Net over F₂ — Constructive and digital

Digital (26, 36, 53)-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 (15, 25, 27)-net over F₂, using
  - 2 times m-reduction [i] based on digital (15, 27, 27)-net over F₂, using
    - a shift-net [i]

(26, 26+10, 69)-Net over F₂ — Digital

Digital (26, 36, 69)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+10, 376)-Net in Base 2 — Upper bound on s

There is no (26, 36, 377)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 69529 296812 > 2³⁶ [i]