MinT - Best Known (131, 131+10, s)-Nets in Base 2

Best Known (131, 131+10, s)-Nets in Base 2

(131, 131+10, 4194301)-Net over F₂ — Constructive and digital

Digital (131, 141, 4194301)-net over F₂, using

2¹ times duplication [i] based on digital (130, 140, 4194301)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2¹⁴⁰, 4194301, F₂, 15, 10) (dual of [(4194301, 15), 62914375, 11]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 10), using
    - strength reduction [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
      - OOAs constructed from BCH codes [i]

(131, 131+10, large)-Net over F₂ — Digital

Digital (131, 141, large)-net over F₂, using

2¹ times duplication [i] based on digital (130, 140, large)-net over F₂, using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 10), using
  - strength reduction [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
    - OOAs constructed from BCH codes [i]

(131, 131+10, large)-Net in Base 2 — Upper bound on s

There is no (131, 141, large)-net in base 2, because

8 times m-reduction [i] would yield (131, 133, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]