MinT - Best Known (37, 37+6, s)-Nets in Base 2

Best Known (37, 37+6, s)-Nets in Base 2

(37, 37+6, 16382)-Net over F₂ — Constructive and digital

Digital (37, 43, 16382)-net over F₂, using

1 times m-reduction [i] based on digital (37, 44, 16382)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2⁴⁴, 16382, F₂, 7, 7) (dual of [(16382, 7), 114630, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁴⁴, 16383, F₂, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(37, 37+6, 16383)-Net over F₂ — Digital

Digital (37, 43, 16383)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁴³, 16383, F₂, 6, 6) (dual of [(16383, 6), 98255, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁴³, 16383, F₂, 5, 6) (dual of [(16383, 5), 81872, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴³, 16383, F₂, 2, 6) (dual of [(16383, 2), 32723, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(37, 37+6, 37505)-Net in Base 2 — Upper bound on s

There is no (37, 43, 37506)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 8 796095 506388 > 2⁴³ [i]