MinT - Information on Result #1204434

Information on Result #1204434

Digital (26, 37, 1677977)-net over F₂₅₆, using net defined by OOA based on linear OOA(256³⁷, 1677977, F₂₅₆, 15, 11) (dual of [(1677977, 15), 25169618, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(256³⁷, 1677978, F₂₅₆, 5, 11) (dual of [(1677978, 5), 8389853, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁶, 258, F₂₅₆, 5, 5) (dual of [(258, 5), 1284, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁶, 258, F₂₅₆, 4, 5) (dual of [(258, 4), 1026, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (1, 6, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256³¹, 1677720, F₂₅₆, 5, 11) (dual of [(1677720, 5), 8388569, 12]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(256³¹, 8388600, F₂₅₆, 11) (dual of [8388600, 8388569, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(256³¹, large, F₂₅₆, 11) (dual of [large, large−31, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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 (137, 148, 6711908)-net over F₄	[i]		Trace Code for Nets
2	Digital (63, 74, 3355954)-net over F₁₆	[i]		Trace Code for Nets