MinT - Information on Result #1847807

Information on Result #1847807

OOA(128⁸, 65538, S₁₂₈, 2, 4), using extracting embedded OOA based on (4, 8, 65538)-net in base 128, using

base change [i] based on digital (3, 7, 65538)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁷, 65538, F₂₅₆, 4, 4) (dual of [(65538, 4), 262145, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(256⁷, 65538, F₂₅₆, 3, 4) (dual of [(65538, 3), 196607, 5]-NRT-code), using
    - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256⁷, 65538, F₂₅₆, 4) (dual of [65538, 65531, 5]-code), using
      - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(256⁷, 65536, F₂₅₆, 4) (dual of [65536, 65529, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(256⁵, 65536, F₂₅₆, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	OOA(128⁹, 65538, S₁₂₈, 2, 4)	[i]		OOA Duplication
2	OOA(128⁸, 65537, S₁₂₈, 3, 4)	[i]		OOA Stacking with Additional Row
3	OOA(128⁸, 65537, S₁₂₈, 4, 4)	[i]		OOA Stacking with Additional Row