MinT - Information on Result #1840368

Information on Result #1840368

OOA(16⁶⁰, 419434, S₁₆, 11, 11), using OOA 5-folding and stacking with additional row based on OA(16⁶⁰, 2097171, S₁₆, 11), using

discarding factors based on OA(16⁶⁰, 2097172, S₁₆, 11), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16⁵, 17, F₁₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,16)), using
    - extended Reedâ€“Solomon code RS_e(12,16) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
  2. OA(16⁵⁵, 2097155, S₁₆, 11), using
    - discarding parts of the base [i] based on linear OA(128³¹, 2097155, F₁₂₈, 11) (dual of [2097155, 2097124, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(49, 60, 419434)-net in base 16	[i]		Net Defined by OOA