MinT - Best Known (27, 40, s)-Nets in Base 2

Best Known (27, 40, s)-Nets in Base 2

(27, 40, 44)-Net over F₂ — Constructive and digital

Digital (27, 40, 44)-net over F₂, using

4 times m-reduction [i] based on digital (27, 44, 44)-net over F₂, using
- a shift-net [i]

(27, 40, 47)-Net over F₂ — Digital

Digital (27, 40, 47)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 40, 262)-Net in Base 2 — Upper bound on s

There is no (27, 40, 263)-net in base 2, because

1 times m-reduction [i] would yield (27, 39, 263)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 554867 200861 > 2³⁹ [i]