MinT - Information on Result #1203152

Information on Result #1203152

Digital (16, 24, 524290)-net over F₁₂₈, using net defined by OOA based on linear OOA(128²⁴, 524290, F₁₂₈, 8, 8) (dual of [(524290, 8), 4194296, 9]-NRT-code), using

OA 4-folding and stacking [i] based on linear OA(128²⁴, 2097160, F₁₂₈, 8) (dual of [2097160, 2097136, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(128²⁴, 2097163, F₁₂₈, 8) (dual of [2097163, 2097139, 9]-code), using
  - constructionÂ X applied to C_e(7) âŠ‚ C_e(4) [i] based on
    1. linear OA(128²², 2097152, F₁₂₈, 8) (dual of [2097152, 2097130, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(128², 11, F₁₂₈, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
      - discarding factors / shortening the dual code based on linear OA(128², 128, F₁₂₈, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
        Reedâ€“Solomon code RS(126,128) [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	(61, 77, 1572865)-net in base 128	[i]	(u,Â u+v)-Construction for Nets
2	(34, 42, 524290)-net in base 16	[i]	Base Change
3	(20, 28, 524290)-net in base 64	[i]	Base Change