MinT - Best Known (144, 153, s)-Nets in Base 2

Best Known (144, 153, s)-Nets in Base 2

(144, 153, 4456446)-Net over F₂ — Constructive and digital

Digital (144, 153, 4456446)-net over F₂, using

2¹ times duplication [i] based on digital (143, 152, 4456446)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2¹⁵², 4456446, F₂, 9, 9) (dual of [(4456446, 9), 40107862, 10]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹⁵², 4456446, F₂, 8, 9) (dual of [(4456446, 8), 35651416, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³⁶, 262145, F₂, 8, 4) (dual of [(262145, 8), 2097124, 5]-NRT-code), using
        appending 4 arbitrary columns [i] based on linear OOA(2³⁶, 262145, F₂, 4, 4) (dual of [(262145, 4), 1048544, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2³⁶, 262145, F₂, 3, 4) (dual of [(262145, 3), 786399, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (32, 36, 262145)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
      2. linear OOA(2¹¹⁶, 4194301, F₂, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁶, large, F₂, 2, 9), using
        OOAs constructed from BCH codes [i]

(144, 153, large)-Net over F₂ — Digital

Digital (144, 153, large)-net over F₂, using

2¹ times duplication [i] based on digital (143, 152, large)-net over F₂, using
- t-expansion [i] based on digital (141, 152, large)-net over F₂, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁵², large, F₂, 3, 11), using
    - 4 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
      - OOAs constructed from BCH codes [i]

(144, 153, large)-Net in Base 2 — Upper bound on s

There is no (144, 153, large)-net in base 2, because

7 times m-reduction [i] would yield (144, 146, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]