MinT - Best Known (49−6, 49, s)-Nets in Base 2

Best Known (49−6, 49, s)-Nets in Base 2

(49−6, 49, 65534)-Net over F₂ — Constructive and digital

Digital (43, 49, 65534)-net over F₂, using

1 times m-reduction [i] based on digital (43, 50, 65534)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2⁵⁰, 65534, F₂, 7, 7) (dual of [(65534, 7), 458688, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁵⁰, 65535, F₂, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(49−6, 49, 65535)-Net over F₂ — Digital

Digital (43, 49, 65535)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁴⁹, 65535, F₂, 6, 6) (dual of [(65535, 6), 393161, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁴⁹, 65535, F₂, 5, 6) (dual of [(65535, 5), 327626, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁹, 65535, F₂, 2, 6) (dual of [(65535, 2), 131021, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(49−6, 49, 150035)-Net in Base 2 — Upper bound on s

There is no (43, 49, 150036)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 562 950119 535543 > 2⁴⁹ [i]