MinT - Information on Result #1194772

Information on Result #1194772

Digital (19, 24, 1044767)-net over F₁₆, using net defined by OOA based on linear OOA(16²⁴, 1044767, F₁₆, 6, 5) (dual of [(1044767, 6), 6268578, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(16²⁴, 1044768, F₁₆, 2, 5) (dual of [(1044768, 2), 2089512, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁰, s, F₁₆, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  3. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  4. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  5. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  6. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  7. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  8. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  9. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  10. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  11. linear OOA(16⁰, 65298, F₁₆, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
  12. linear OOA(16¹, 65298, F₁₆, 2, 1) (dual of [(65298, 2), 130595, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16¹, s, F₁₆, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  13. linear OOA(16¹, 65298, F₁₆, 2, 1) (dual of [(65298, 2), 130595, 2]-NRT-code) (see above)
  14. linear OOA(16¹, 65298, F₁₆, 2, 1) (dual of [(65298, 2), 130595, 2]-NRT-code) (see above)
  15. linear OOA(16⁵, 65298, F₁₆, 2, 2) (dual of [(65298, 2), 130591, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁵, 69905, F₁₆, 2, 2) (dual of [(69905, 2), 139805, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
        Hamming code H(5,16) [i]
  16. linear OOA(16¹⁶, 65298, F₁₆, 2, 5) (dual of [(65298, 2), 130580, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(16², 17, F₁₆, 2, 2) (dual of [(17, 2), 32, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;32,16) [i]
      2. linear OOA(16¹⁴, 65281, F₁₆, 2, 5) (dual of [(65281, 2), 130548, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
        trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (70, 80, 4400207)-net over F₁₆	[i]		(u,Â u+v)-Construction for Nets
2	Digital (75, 86, 4400207)-net over F₁₆	[i]		(u,Â u+v)-Construction for Nets