MinT - Information on Result #3329859

Information on Result #3329859

(13, 23, 20651)-net in base 128, using 1 times m-reduction based on (13, 24, 20651)-net in base 128, using

base change [i] based on digital (10, 21, 20651)-net over F₂₅₆, using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(256²¹, 20651, F₂₅₆, 3, 11) (dual of [(20651, 3), 61932, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(256²¹, 21846, F₂₅₆, 3, 11) (dual of [(21846, 3), 65517, 12]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(256²¹, 65538, F₂₅₆, 11) (dual of [65538, 65517, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(256²¹, 65536, F₂₅₆, 11) (dual of [65536, 65515, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(256¹⁹, 65536, F₂₅₆, 10) (dual of [65536, 65517, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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: Arbitrary.

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	OOA(128²³, 20651, S₁₂₈, 4, 10)	[i]		Extracting Embedded OOA