MinT - Best Known (51, 51+16, s)-Nets in Base 2

Best Known (51, 51+16, s)-Nets in Base 2

(51, 51+16, 87)-Net over F₂ — Constructive and digital

Digital (51, 67, 87)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (13, 21, 39)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (30, 46, 48)-net over F₂, using
  - 2 times m-reduction [i] based on digital (30, 48, 48)-net over F₂, using
    - a shift-net [i]

(51, 51+16, 143)-Net over F₂ — Digital

Digital (51, 67, 143)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+16, 1238)-Net in Base 2 — Upper bound on s

There is no (51, 67, 1239)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 148 258423 220776 694402 > 2⁶⁷ [i]