MinT - Information on Result #1842194

Information on Result #1842194

(174, 184, 6291464)-net in base 2, using (u,Â u+v)-construction based on

(40, 45, 2097163)-net in base 2, using
- net defined by OOA [i] based on OOA(2⁴⁵, 2097163, S₂, 5, 5), using
  - OOA 2-folding and stacking with additional row [i] based on OA(2⁴⁵, 4194327, S₂, 5), using
    - constructionÂ X4 applied to RM(1,22) âŠ‚ K(22) [i] based on
      1. OA(2⁴⁴, 4194304, S₂, 5), using Kerdock OA K(22) [i]
      2. linear OA(2²³, 4194304, F₂, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,2)), using Reedâ€“Muller code RM(1,22) [i]
      3. linear OA(2²², 23, F₂, 21) (dual of [23, 1, 22]-code), using
        strength reduction [i] based on linear OA(2²², 23, F₂, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
        dual of repetition code with length 23 [i]
      4. linear OA(2¹, 23, F₂, 1) (dual of [23, 22, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
digital (129, 139, 4194301)-net over F₂, using
- 1 times m-reduction [i] based on 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]

None.

None.