MinT - Best Known (62−16, 62, s)-Nets in Base 2

Best Known (62−16, 62, s)-Nets in Base 2

(62−16, 62, 80)-Net over F₂ — Constructive and digital

Digital (46, 62, 80)-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 (25, 41, 41)-net over F₂, using
  - a shift-net [i]

(62−16, 62, 109)-Net over F₂ — Digital

Digital (46, 62, 109)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−16, 62, 798)-Net in Base 2 — Upper bound on s

There is no (46, 62, 799)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4 615254 918552 010573 > 2⁶² [i]