MinT - Information on Result #1204576

Information on Result #1204576

Digital (31, 44, 1398357)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁴⁴, 1398357, F₂₅₆, 18, 13) (dual of [(1398357, 18), 25170382, 14]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(256⁴⁴, 1398358, F₂₅₆, 6, 13) (dual of [(1398358, 6), 8390104, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁷, 258, F₂₅₆, 6, 6) (dual of [(258, 6), 1541, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁷, 258, F₂₅₆, 5, 6) (dual of [(258, 5), 1283, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (1, 7, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256³⁷, 1398100, F₂₅₆, 6, 13) (dual of [(1398100, 6), 8388563, 14]-NRT-code), using
    - OOA 6-folding [i] based on linear OA(256³⁷, 8388600, F₂₅₆, 13) (dual of [8388600, 8388563, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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 (163, 176, 5593428)-net over F₄	[i]		Trace Code for Nets
2	Digital (75, 88, 2796714)-net over F₁₆	[i]		Trace Code for Nets