MinT - Information on Result #1204704

Information on Result #1204704

Digital (40, 56, 1048704)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁵⁶, 1048704, F₂₅₆, 20, 16) (dual of [(1048704, 20), 20974024, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(256⁵⁶, 2097409, F₂₅₆, 4, 16) (dual of [(2097409, 4), 8389580, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹⁰, 259, F₂₅₆, 4, 8) (dual of [(259, 4), 1026, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 10, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [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 (208, 224, 4194816)-net over F₄	[i]		Trace Code for Nets
2	Digital (96, 112, 2097408)-net over F₁₆	[i]		Trace Code for Nets