MinT - Information on Result #1181334

Information on Result #1181334

Digital (106, 123, 4098)-net over F₂, using net defined by OOA based on linear OOA(2¹²³, 4098, F₂, 17, 17) (dual of [(4098, 17), 69543, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(2¹²³, 32785, F₂, 17) (dual of [32785, 32662, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹²³, 32786, F₂, 17) (dual of [32786, 32663, 18]-code), using
  - adding a parity check bit [i] based on linear OA(2¹²², 32785, F₂, 16) (dual of [32785, 32663, 17]-code), using
    - constructionÂ X4 applied to C([0,16]) âŠ‚ C([1,14]) [i] based on
      1. linear OA(2¹²¹, 32767, F₂, 17) (dual of [32767, 32646, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(2¹⁰⁵, 32767, F₂, 14) (dual of [32767, 32662, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
        dual of repetition code with length 18 [i]
      4. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 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]

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		Method
1	Digital (107, 123, 4098)-net over F₂	[i]	t-Expansion
2	Digital (107, 124, 4098)-net over F₂	[i]	Net Duplication
3	Digital (108, 125, 4098)-net over F₂	[i]
4	Digital (109, 126, 4098)-net over F₂	[i]