MinT - Information on Result #1754913

Information on Result #1754913

Digital (172, 195, 21852)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁵, 21852, F₂, 6, 23) (dual of [(21852, 6), 130917, 24]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁹⁵, 131112, F₂, 23) (dual of [131112, 130917, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁹⁵, 131113, F₂, 23) (dual of [131113, 130918, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
    1. linear OA(2¹⁸⁸, 131072, F₂, 23) (dual of [131072, 130884, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(2¹⁵⁴, 131072, F₂, 19) (dual of [131072, 130918, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2⁷, 41, F₂, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]

Mode: 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 (173, 196, 21852)-net over F₂	[i]		Net Duplication
2	Digital (174, 197, 21852)-net over F₂	[i]
3	Digital (175, 198, 21852)-net over F₂	[i]