MinT - Best Known (53−17, 53, s)-Nets in Base 2

Best Known (53−17, 53, s)-Nets in Base 2

(53−17, 53, 51)-Net over F₂ — Constructive and digital

Digital (36, 53, 51)-net over F₂, using

2² times duplication [i] based on digital (34, 51, 51)-net over F₂, using
- t-expansion [i] based on digital (33, 51, 51)-net over F₂, using
  - a shift-net [i]

(53−17, 53, 58)-Net over F₂ — Digital

Digital (36, 53, 58)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−17, 53, 329)-Net in Base 2 — Upper bound on s

There is no (36, 53, 330)-net in base 2, because

1 times m-reduction [i] would yield (36, 52, 330)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4569 681231 993857 > 2⁵² [i]