MinT - Information on Result #1203380

Information on Result #1203380

Digital (24, 36, 349527)-net over F₁₂₈, using net defined by OOA based on linear OOA(128³⁶, 349527, F₁₂₈, 12, 12) (dual of [(349527, 12), 4194288, 13]-NRT-code), using

OA 6-folding and stacking [i] based on linear OA(128³⁶, 2097162, F₁₂₈, 12) (dual of [2097162, 2097126, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(128³⁶, 2097163, F₁₂₈, 12) (dual of [2097163, 2097127, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(8) [i] based on
    1. linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(128²⁵, 2097152, F₁₂₈, 9) (dual of [2097152, 2097127, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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	Digital (25, 37, 349527)-net over F₁₂₈	[i]	Net Duplication
2	(51, 63, 349527)-net in base 16	[i]	Base Change
3	(30, 42, 349527)-net in base 64	[i]	Base Change