MinT - Information on Result #1841973

Information on Result #1841973

(24, 41, 8193)-net in base 128, using net defined by OOA based on OOA(128⁴¹, 8193, S₁₂₈, 17, 17), using

OOA 8-folding and stacking with additional row [i] based on OA(128⁴¹, 65545, S₁₂₈, 17), using
- 1 times code embedding in larger space [i] based on OA(128⁴⁰, 65544, S₁₂₈, 17), using
  - discarding parts of the base [i] based on linear OA(256³⁵, 65544, F₂₅₆, 17) (dual of [65544, 65509, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(13) [i] based on
      1. linear OA(256³³, 65536, F₂₅₆, 17) (dual of [65536, 65503, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
        discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [i]

Mode: Constructive.

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	(25, 41, 8193)-net in base 128	[i]		t-Expansion
2	(25, 42, 8193)-net in base 128	[i]		Net Duplication
3	(26, 43, 8193)-net in base 128	[i]		Net Duplication