MinT - Information on Result #1207985

Information on Result #1207985

Digital (127, 138, 1913228)-net over F₃, using (u,Â u+v)-construction based on

digital (5, 10, 38)-net over F₃, using
- linear code embedding found in a computer search [i]
digital (117, 128, 1913190)-net over F₃, using
- trace code for nets [i] based on digital (53, 64, 956595)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁶⁴, 956595, F₉, 11, 11) (dual of [(956595, 11), 10522481, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(9⁶⁴, 4782976, F₉, 11) (dual of [4782976, 4782912, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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 and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹³⁸, 1913228, F₃, 5, 11) (dual of [(1913228, 5), 9566002, 12]-NRT-code)	[i]		Extracting Embedded OOA