MinT - Information on Result #1204710

Information on Result #1204710

Digital (44, 60, 1048960)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁶⁰, 1048960, F₂₅₆, 20, 16) (dual of [(1048960, 20), 20979140, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(256⁶⁰, 2097921, F₂₅₆, 4, 16) (dual of [(2097921, 4), 8391624, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹⁴, 771, F₂₅₆, 4, 8) (dual of [(771, 4), 3070, 9]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(256², 257, F₂₅₆, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1026,256) [i]
      2. 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]
      3. 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 (224, 240, 4195840)-net over F₄	[i]		Trace Code for Nets
2	Digital (104, 120, 2097920)-net over F₁₆	[i]		Trace Code for Nets