MinT - Information on Result #1204706

Information on Result #1204706

Digital (42, 58, 1048831)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁵⁸, 1048831, F₂₅₆, 20, 16) (dual of [(1048831, 20), 20976562, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(256⁵⁸, 2097663, F₂₅₆, 4, 16) (dual of [(2097663, 4), 8390594, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(256⁵⁸, 2097664, F₂₅₆, 4, 16) (dual of [(2097664, 4), 8390598, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256¹², 514, F₂₅₆, 4, 8) (dual of [(514, 4), 2044, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        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]
        linear OOA(256⁸, 257, F₂₅₆, 4, 8) (dual of [(257, 4), 1020, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1020,256) [i]
    2. linear OOA(256⁴⁶, 2097150, F₂₅₆, 4, 16) (dual of [(2097150, 4), 8388554, 17]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(256⁴⁶, 8388600, F₂₅₆, 16) (dual of [8388600, 8388554, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁴⁶, large, F₂₅₆, 16) (dual of [large, large−46, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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		This result only	Method
1	Digital (216, 232, 4195324)-net over F₄	[i]		Trace Code for Nets
2	Digital (100, 116, 2097662)-net over F₁₆	[i]		Trace Code for Nets