MinT - Best Known (61, 61+6, s)-Nets in Base 2

Best Known (61, 61+6, s)-Nets in Base 2

(61, 61+6, 4194302)-Net over F₂ — Constructive and digital

Digital (61, 67, 4194302)-net over F₂, using

1 times m-reduction [i] based on digital (61, 68, 4194302)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2⁶⁸, 4194302, F₂, 7, 7) (dual of [(4194302, 7), 29360046, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(61, 61+6, 4194303)-Net over F₂ — Digital

Digital (61, 67, 4194303)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁶⁷, 4194303, F₂, 6, 6) (dual of [(4194303, 6), 25165751, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁶⁷, 4194303, F₂, 5, 6) (dual of [(4194303, 5), 20971448, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁶⁷, 4194303, F₂, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(61, 61+6, large)-Net in Base 2 — Upper bound on s

There is no (61, 67, large)-net in base 2, because

4 times m-reduction [i] would yield (61, 63, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]