MinT - Information on Result #1204380

Information on Result #1204380

Digital (27, 37, 1710616)-net over F₂₅₆, using net defined by OOA based on linear OOA(256³⁷, 1710616, F₂₅₆, 15, 10) (dual of [(1710616, 15), 25659203, 11]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(256³⁷, 1710617, F₂₅₆, 5, 10) (dual of [(1710617, 5), 8553048, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁹, 32897, F₂₅₆, 5, 5) (dual of [(32897, 5), 164476, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁹, 32897, F₂₅₆, 4, 5) (dual of [(32897, 4), 131579, 6]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        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]
        linear OOA(256⁷, 32640, F₂₅₆, 4, 5) (dual of [(32640, 4), 130553, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(256²⁸, 1677720, F₂₅₆, 5, 10) (dual of [(1677720, 5), 8388572, 11]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(256²⁸, 8388600, F₂₅₆, 10) (dual of [8388600, 8388572, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(256²⁸, large, F₂₅₆, 10) (dual of [large, large−28, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (138, 148, 6842464)-net over F₄	[i]		Trace Code for Nets
2	Digital (64, 74, 3421232)-net over F₁₆	[i]		Trace Code for Nets