MinT - Information on Result #1204322

Information on Result #1204322

Digital (20, 29, 2097406)-net over F₂₅₆, using net defined by OOA based on linear OOA(256²⁹, 2097406, F₂₅₆, 12, 9) (dual of [(2097406, 12), 25168843, 10]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(256²⁹, 2097407, F₂₅₆, 4, 9) (dual of [(2097407, 4), 8389599, 10]-NRT-code), using
- (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(256²⁵, 2097150, F₂₅₆, 4, 9) (dual of [(2097150, 4), 8388575, 10]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(256²⁵, 8388600, F₂₅₆, 9) (dual of [8388600, 8388575, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(256²⁵, large, F₂₅₆, 9) (dual of [large, large−25, 10]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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 (107, 116, large)-net over F₄	[i]		Trace Code for Nets
2	Digital (49, 58, 4194812)-net over F₁₆	[i]		Trace Code for Nets