MinT - Information on Result #3180005

Information on Result #3180005

Digital (80, 92, 5464)-net over F₂, using t-expansion based on digital (79, 92, 5464)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁹², 5464, F₂, 13, 13) (dual of [(5464, 13), 70940, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2⁹², 32785, F₂, 13) (dual of [32785, 32693, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(2⁷⁶, 32768, F₂, 11) (dual of [32768, 32692, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
      - strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
    4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (81, 93, 5464)-net over F₂	[i]		Net Duplication
2	Digital (82, 94, 5464)-net over F₂	[i]
3	Digital (83, 95, 5464)-net over F₂	[i]