MinT - Information on Result #1205308

Information on Result #1205308

Digital (238, 252, large)-net over F₄, using trace code for nets based on digital (49, 63, 2097278)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256⁶³, 2097278, F₂₅₆, 20, 14) (dual of [(2097278, 20), 41945497, 15]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(256⁶³, 4194557, F₂₅₆, 4, 14) (dual of [(4194557, 4), 16778165, 15]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(256⁴, 257, F₂₅₆, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(4;1024,256) [i]
    2. linear OOA(256¹⁹, 2097150, F₂₅₆, 4, 7) (dual of [(2097150, 4), 8388581, 8]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(256¹⁹, 2796200, F₂₅₆, 4, 7) (dual of [(2796200, 4), 11184781, 8]-NRT-code), using
        OOA 3-folding and stacking with additional row [i] based on linear OA(256¹⁹, 8388601, F₂₅₆, 7) (dual of [8388601, 8388582, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹⁹, large, F₂₅₆, 7) (dual of [large, large−19, 8]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    3. linear OOA(256⁴⁰, 2097150, F₂₅₆, 4, 14) (dual of [(2097150, 4), 8388560, 15]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(256⁴⁰, 8388600, F₂₅₆, 14) (dual of [8388600, 8388560, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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 (239, 252, large)-net over F₄	[i]	t-Expansion
2	Digital (240, 252, large)-net over F₄	[i]
3	Digital (241, 252, large)-net over F₄	[i]
4	Digital (242, 252, large)-net over F₄	[i]
5	Digital (243, 252, large)-net over F₄	[i]
6	Digital (244, 252, large)-net over F₄	[i]
7	Digital (245, 252, large)-net over F₄	[i]
8	Digital (246, 252, large)-net over F₄	[i]
9	Digital (247, 252, large)-net over F₄	[i]
10	Digital (248, 252, large)-net over F₄	[i]
11	Digital (249, 252, large)-net over F₄	[i]
12	Digital (239, 253, large)-net over F₄	[i]	Net Duplication
13	Digital (240, 254, large)-net over F₄	[i]
14	Digital (241, 255, large)-net over F₄	[i]
15	Digital (242, 256, large)-net over F₄	[i]
16	Digital (243, 257, large)-net over F₄	[i]
17	Digital (244, 258, large)-net over F₄	[i]
18	Digital (245, 259, large)-net over F₄	[i]
19	Digital (246, 260, large)-net over F₄	[i]
20	Digital (238, 251, large)-net over F₄	[i]	m-Reduction
21	Digital (238, 250, large)-net over F₄	[i]
22	Digital (238, 249, large)-net over F₄	[i]
23	Digital (238, 248, large)-net over F₄	[i]
24	Digital (238, 247, large)-net over F₄	[i]
25	Digital (238, 246, large)-net over F₄	[i]
26	Digital (238, 245, large)-net over F₄	[i]
27	Digital (238, 244, large)-net over F₄	[i]
28	Digital (238, 243, large)-net over F₄	[i]
29	Digital (238, 242, large)-net over F₄	[i]
30	Digital (238, 241, large)-net over F₄	[i]