MinT - Information on Result #1203974

Information on Result #1203974

Digital (44, 66, 190651)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁶, 190651, F₁₂₈, 22, 22) (dual of [(190651, 22), 4194256, 23]-NRT-code), using

OA 11-folding and stacking [i] based on linear OA(128⁶⁶, 2097161, F₁₂₈, 22) (dual of [2097161, 2097095, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁶⁶, 2097163, F₁₂₈, 22) (dual of [2097163, 2097097, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
    1. linear OA(128⁶⁴, 2097152, F₁₂₈, 22) (dual of [2097152, 2097088, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(128⁵⁵, 2097152, F₁₂₈, 19) (dual of [2097152, 2097097, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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		This result only	Method
1	Digital (45, 67, 190651)-net over F₁₂₈	[i]		Net Duplication
2	(55, 77, 190651)-net in base 64	[i]		Base Change