MinT - Information on Result #1823556

Information on Result #1823556

(29, 36, 43692)-net in base 8, using base change based on digital (20, 27, 43692)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16²⁷, 43692, F₁₆, 7, 7) (dual of [(43692, 7), 305817, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(16²⁷, 131077, F₁₆, 7) (dual of [131077, 131050, 8]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(16²⁶, 131076, F₁₆, 7) (dual of [131076, 131050, 8]-code), using
    - trace code [i] based on linear OA(256¹³, 65538, F₂₅₆, 7) (dual of [65538, 65525, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(256¹³, 65536, F₂₅₆, 7) (dual of [65536, 65523, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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	(128, 142, 2440434)-net in base 8	[i]		(u,Â u+v)-Construction for Nets
2	(135, 150, 2440434)-net in base 8	[i]		(u,Â u+v)-Construction for Nets