MinT - Best Known (152−11, 152, s)-Nets in Base 2

Best Known (152−11, 152, s)-Nets in Base 2

(152−11, 152, 4194337)-Net over F₂ — Constructive and digital

Digital (141, 152, 4194337)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 12, 36)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (129, 140, 4194301)-net over F₂, using
  - net defined by OOA [i] based on linear OOA(2¹⁴⁰, 4194301, F₂, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
      - OOAs constructed from BCH codes [i]

(152−11, 152, large)-Net over F₂ — Digital

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]

(152−11, 152, large)-Net in Base 2 — Upper bound on s

There is no (141, 152, large)-net in base 2, because

9 times m-reduction [i] would yield (141, 143, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]