MinT - Information on Result #1823676

Information on Result #1823676

(70, 88, 7282)-net in base 8, using base change based on digital (48, 66, 7282)-net over F₁₆, using

16¹ times duplication [i] based on digital (47, 65, 7282)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁶⁵, 7282, F₁₆, 18, 18) (dual of [(7282, 18), 131011, 19]-NRT-code), using
  - OA 9-folding and stacking [i] based on linear OA(16⁶⁵, 65538, F₁₆, 18) (dual of [65538, 65473, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(16⁶⁵, 65540, F₁₆, 18) (dual of [65540, 65475, 19]-code), using
      - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
        linear OA(16⁶⁵, 65536, F₁₆, 18) (dual of [65536, 65471, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
        linear OA(16⁶¹, 65536, F₁₆, 17) (dual of [65536, 65475, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 16⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(16⁰, 4, F₁₆, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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	(71, 89, 7282)-net in base 8	[i]		Net Duplication
2	(72, 90, 7282)-net in base 8	[i]		Net Duplication