MinT - Best Known (30, 42, s)-Nets in Base 2

Best Known (30, 42, s)-Nets in Base 2

(30, 42, 55)-Net over F₂ — Constructive and digital

Digital (30, 42, 55)-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 (16, 28, 29)-net over F₂, using
  - 1 times m-reduction [i] based on digital (16, 29, 29)-net over F₂, using
    - a shift-net [i]

(30, 42, 67)-Net over F₂ — Digital

Digital (30, 42, 67)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 42, 374)-Net in Base 2 — Upper bound on s

There is no (30, 42, 375)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4 412732 846201 > 2⁴² [i]