MinT - Information on Result #1203768

Information on Result #1203768

Digital (36, 54, 233018)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁵⁴, 233018, F₁₂₈, 18, 18) (dual of [(233018, 18), 4194270, 19]-NRT-code), using

OA 9-folding and stacking [i] based on linear OA(128⁵⁴, 2097162, F₁₂₈, 18) (dual of [2097162, 2097108, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁵⁴, 2097163, F₁₂₈, 18) (dual of [2097163, 2097109, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(14) [i] based on
    1. linear OA(128⁵², 2097152, F₁₂₈, 18) (dual of [2097152, 2097100, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(128⁴³, 2097152, F₁₂₈, 15) (dual of [2097152, 2097109, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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 (37, 55, 233018)-net over F₁₂₈	[i]		Net Duplication
2	(45, 63, 233018)-net in base 64	[i]		Base Change