MinT - Information on Result #1218800

Information on Result #1218800

Digital (67, 78, 3420737)-net over F₁₆, using (u,Â u+v)-construction based on

digital (11, 16, 65297)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16¹⁶, 65297, F₁₆, 6, 5) (dual of [(65297, 6), 391766, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(16¹⁶, 65298, F₁₆, 2, 5) (dual of [(65298, 2), 130580, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(16², 17, F₁₆, 2, 2) (dual of [(17, 2), 32, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;32,16) [i]
      2. linear OOA(16¹⁴, 65281, F₁₆, 2, 5) (dual of [(65281, 2), 130548, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
        trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
digital (51, 62, 3355440)-net over F₁₆, using
- trace code for nets [i] based on digital (20, 31, 1677720)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256³¹, 1677720, F₂₅₆, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(256³¹, 8388601, F₂₅₆, 11) (dual of [8388601, 8388570, 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	(93, 104, 3420737)-net in base 8	[i]		Base Change