MinT - Information on Result #1208115

Information on Result #1208115

Digital (231, 243, large)-net over F₃, using (u,Â u+v)-construction based on

digital (57, 63, 2796205)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁶³, 2796205, F₃, 6, 6) (dual of [(2796205, 6), 16777167, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁶³, 2796205, F₃, 5, 6) (dual of [(2796205, 5), 13980962, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3³, 4, F₃, 5, 3) (dual of [(4, 5), 17, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(5;17,3) [i]
      2. linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
        OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (168, 180, 5592400)-net over F₃, using
- trace code for nets [i] based on digital (78, 90, 2796200)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁹⁰, 2796200, F₉, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OOA(9⁹⁰, 8388601, F₉, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(9⁹⁰, 8388602, F₉, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
        trace code [i] based on linear OOA(81⁴⁵, 4194301, F₈₁, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁵, 8388602, F₈₁, 12) (dual of [8388602, 8388557, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (232, 243, large)-net over F₃	[i]	t-Expansion
2	Digital (233, 243, large)-net over F₃	[i]
3	Digital (234, 243, large)-net over F₃	[i]
4	Digital (235, 243, large)-net over F₃	[i]
5	Digital (236, 243, large)-net over F₃	[i]
6	Digital (237, 243, large)-net over F₃	[i]
7	Digital (238, 243, large)-net over F₃	[i]
8	Digital (239, 243, large)-net over F₃	[i]
9	Digital (240, 243, large)-net over F₃	[i]
10	Digital (232, 244, large)-net over F₃	[i]	Net Duplication
11	Digital (233, 245, large)-net over F₃	[i]
12	Digital (234, 246, large)-net over F₃	[i]
13	Digital (235, 247, large)-net over F₃	[i]
14	Digital (236, 248, large)-net over F₃	[i]
15	Digital (237, 249, large)-net over F₃	[i]
16	Digital (238, 250, large)-net over F₃	[i]
17	Digital (231, 242, large)-net over F₃	[i]	m-Reduction
18	Digital (231, 241, large)-net over F₃	[i]
19	Digital (231, 240, large)-net over F₃	[i]
20	Digital (231, 239, large)-net over F₃	[i]
21	Digital (231, 238, large)-net over F₃	[i]
22	Digital (231, 237, large)-net over F₃	[i]
23	Digital (231, 236, large)-net over F₃	[i]
24	Digital (231, 235, large)-net over F₃	[i]
25	Digital (231, 234, large)-net over F₃	[i]
26	Linear OOA(3²⁴³, large, F₃, 5, 12)	[i]	Extracting Embedded OOA