MinT - Best Known (48−15, 48, s)-Nets in Base 2

Best Known (48−15, 48, s)-Nets in Base 2

(48−15, 48, 51)-Net over F₂ — Constructive and digital

Digital (33, 48, 51)-net over F₂, using

3 times m-reduction [i] based on digital (33, 51, 51)-net over F₂, using
- a shift-net [i]

(48−15, 48, 57)-Net over F₂ — Digital

Digital (33, 48, 57)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(48−15, 48, 345)-Net in Base 2 — Upper bound on s

There is no (33, 48, 346)-net in base 2, because

1 times m-reduction [i] would yield (33, 47, 346)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 143 442331 862524 > 2⁴⁷ [i]