MinT - Information on Result #1198584

Information on Result #1198584

Digital (53, 82, 1406)-net over F₂₇, using net defined by OOA based on linear OOA(27⁸², 1406, F₂₇, 29, 29) (dual of [(1406, 29), 40692, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(27⁸², 19685, F₂₇, 29) (dual of [19685, 19603, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁸², 19686, F₂₇, 29) (dual of [19686, 19604, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
    1. linear OA(27⁸², 19683, F₂₇, 29) (dual of [19683, 19601, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(27⁷⁹, 19683, F₂₇, 28) (dual of [19683, 19604, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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 and linear.

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		Method
1	Digital (54, 82, 1406)-net over F₂₇	[i]	t-Expansion
2	Digital (54, 83, 1406)-net over F₂₇	[i]	Net Duplication
3	Digital (55, 84, 1406)-net over F₂₇	[i]
4	Digital (56, 85, 1406)-net over F₂₇	[i]
5	Digital (53, 81, 1406)-net over F₂₇	[i]	m-Reduction
6	Digital (67, 96, 1434)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
7	Digital (68, 97, 1444)-net over F₂₇	[i]
8	Digital (69, 98, 1454)-net over F₂₇	[i]
9	Digital (70, 99, 1458)-net over F₂₇	[i]
10	Digital (71, 100, 1470)-net over F₂₇	[i]
11	Digital (72, 101, 1474)-net over F₂₇	[i]
12	Digital (73, 102, 1482)-net over F₂₇	[i]
13	Digital (74, 103, 1488)-net over F₂₇	[i]
14	Digital (75, 104, 1490)-net over F₂₇	[i]
15	Digital (76, 105, 1494)-net over F₂₇	[i]
16	Digital (77, 106, 1500)-net over F₂₇	[i]
17	Digital (78, 107, 1502)-net over F₂₇	[i]
18	Digital (79, 108, 1508)-net over F₂₇	[i]
19	(72, 101, 1488)-net in base 27	[i]
20	(73, 102, 1506)-net in base 27	[i]
21	(75, 104, 1522)-net in base 27	[i]
22	(77, 106, 1556)-net in base 27	[i]
23	(79, 108, 1566)-net in base 27	[i]
24	(94, 123, 1406)-net in base 9	[i]	Base Change