MinT - Information on Result #1204748

Information on Result #1204748

Digital (40, 57, 1048703)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁵⁷, 1048703, F₂₅₆, 20, 17) (dual of [(1048703, 20), 20974003, 18]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(256⁵⁷, 2097407, F₂₅₆, 4, 17) (dual of [(2097407, 4), 8389571, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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(256⁴⁹, 2097150, F₂₅₆, 4, 17) (dual of [(2097150, 4), 8388551, 18]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(256⁴⁹, 8388600, F₂₅₆, 17) (dual of [8388600, 8388551, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(256⁴⁹, large, F₂₅₆, 17) (dual of [large, large−49, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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 (211, 228, 4194812)-net over F₄	[i]		Trace Code for Nets
2	Digital (97, 114, 2097406)-net over F₁₆	[i]		Trace Code for Nets