MinT - Information on Result #548051

Information on Result #548051

There is no linear OA(25⁹⁴, 164, F₂₅, 90) (dual of [164, 70, 91]-code), because constructionÂ Y1 would yield

OA(25⁹³, 97, S₂₅, 90), but
- the linear programming bound shows that MÂ â‰¥ 917 366046 106511 319204 310488 250559 166131 581647 062117 601772 786429 813888 045207 279411 397468 873458 869997 872255 908077 931962 907314 300537 109375 / 81263 > 25⁹³ [i]
linear OA(25⁷⁰, 164, F₂₅, 67) (dual of [164, 94, 68]-code), but
- discarding factors / shortening the dual code would yield linear OA(25⁷⁰, 148, F₂₅, 67) (dual of [148, 78, 68]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(25⁶⁹, 73, S₂₅, 67), but
      - the linear programming bound shows that MÂ â‰¥ 24178 564222 846123 668546 399721 917528 895562 151649 914153 732205 158997 548011 257094 913162 291049 957275 390625 / 7242 > 25⁶⁹ [i]
    2. linear OA(25⁷⁸, 148, F₂₅, 75) (dual of [148, 70, 76]-code), but
      - discarding factors / shortening the dual code would yield linear OA(25⁷⁸, 103, F₂₅, 75) (dual of [103, 25, 76]-code), but
        residual code [i] would yield OA(25³, 27, S₂₅, 3), but
        bound for OAs with index unity [i]

Mode: Bound (linear).

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		Method
1	No linear OA(25⁹⁵, 165, F₂₅, 91) (dual of [165, 70, 92]-code)	[i]	Truncation
2	No linear OA(25⁹⁶, 166, F₂₅, 92) (dual of [166, 70, 93]-code)	[i]
3	No linear OA(25⁹⁷, 167, F₂₅, 93) (dual of [167, 70, 94]-code)	[i]
4	No linear OA(25⁹⁸, 168, F₂₅, 94) (dual of [168, 70, 95]-code)	[i]
5	No linear OA(25⁹⁹, 169, F₂₅, 95) (dual of [169, 70, 96]-code)	[i]
6	No linear OA(25¹⁰⁰, 170, F₂₅, 96) (dual of [170, 70, 97]-code)	[i]
7	No linear OA(25¹⁰¹, 171, F₂₅, 97) (dual of [171, 70, 98]-code)	[i]
8	No linear OA(25¹⁰², 172, F₂₅, 98) (dual of [172, 70, 99]-code)	[i]
9	No linear OA(25¹⁰³, 173, F₂₅, 99) (dual of [173, 70, 100]-code)	[i]
10	No linear OOA(25⁹⁵, 164, F₂₅, 2, 91) (dual of [(164, 2), 233, 92]-NRT-code)	[i]	m-Reduction for OOAs
11	No linear OOA(25⁹⁶, 164, F₂₅, 2, 92) (dual of [(164, 2), 232, 93]-NRT-code)	[i]
12	No linear OOA(25⁹⁷, 164, F₂₅, 2, 93) (dual of [(164, 2), 231, 94]-NRT-code)	[i]
13	No linear OOA(25⁹⁸, 164, F₂₅, 2, 94) (dual of [(164, 2), 230, 95]-NRT-code)	[i]
14	No linear OOA(25⁹⁹, 164, F₂₅, 2, 95) (dual of [(164, 2), 229, 96]-NRT-code)	[i]
15	No linear OOA(25¹⁰⁰, 164, F₂₅, 2, 96) (dual of [(164, 2), 228, 97]-NRT-code)	[i]
16	No linear OOA(25¹⁰¹, 164, F₂₅, 2, 97) (dual of [(164, 2), 227, 98]-NRT-code)	[i]
17	No linear OOA(25¹⁰², 164, F₂₅, 2, 98) (dual of [(164, 2), 226, 99]-NRT-code)	[i]
18	No linear OOA(25¹⁰³, 164, F₂₅, 2, 99) (dual of [(164, 2), 225, 100]-NRT-code)	[i]
19	No linear OOA(25⁹⁴, 164, F₂₅, 2, 90) (dual of [(164, 2), 234, 91]-NRT-code)	[i]	Depth Reduction
20	No digital (4, 94, 164)-net over F₂₅	[i]	Extracting Embedded Orthogonal Array