MinT - Best Known (47−13, 47, s)-Nets in Base 2

Best Known (47−13, 47, s)-Nets in Base 2

(47−13, 47, 66)-Net over F₂ — Constructive and digital

Digital (34, 47, 66)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 15, 36)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (19, 32, 33)-net over F₂, using
  - 1 times m-reduction [i] based on digital (19, 33, 33)-net over F₂, using
    - a shift-net [i]

(47−13, 47, 80)-Net over F₂ — Digital

Digital (34, 47, 80)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁷, 80, F₂, 2, 13) (dual of [(80, 2), 113, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2⁴⁷, 160, F₂, 13) (dual of [160, 113, 14]-code), using
  - a â€œGraâ€ code from Grasslâ€™s database [i]

(47−13, 47, 599)-Net in Base 2 — Upper bound on s

There is no (34, 47, 600)-net in base 2, because

1 times m-reduction [i] would yield (34, 46, 600)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 70 471085 327171 > 2⁴⁶ [i]