MinT - Best Known (226−11, 226, s)-Nets in Base 2

Best Known (226−11, 226, s)-Nets in Base 2

(226−11, 226, large)-Net over F₂ — Constructive and digital

Digital (215, 226, large)-net over F₂, using

2³⁵ times duplication [i] based on digital (180, 191, large)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (41, 46, 4194305)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
  2. digital (134, 145, 4194304)-net over F₂, using
    - (u,Â u+v)-construction [i] based on
      1. digital (0, 5, 3)-net over F₂, using
        net from sequence [i] based on digital (0, 2)-sequence over F₂, using
        Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 0 and N(F) ≥ 3, using
        the rational function field F₂(x) [i]
        Niederreiter sequence [i]
        Sobol sequence [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]

(226−11, 226, large)-Net in Base 2 — Upper bound on s

There is no (215, 226, large)-net in base 2, because

9 times m-reduction [i] would yield (215, 217, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]