MinT - Information on Result #1757828

Information on Result #1757828

Digital (203, 233, 6561)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³³, 6561, F₂, 5, 30) (dual of [(6561, 5), 32572, 31]-NRT-code), using

OOA 5-folding [i] based on linear OA(2²³³, 32805, F₂, 30) (dual of [32805, 32572, 31]-code), using
- strength reduction [i] based on linear OA(2²³³, 32805, F₂, 31) (dual of [32805, 32572, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
    1. linear OA(2²²⁶, 32768, F₂, 31) (dual of [32768, 32542, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    3. linear OA(2⁷, 37, F₂, 3) (dual of [37, 30, 4]-code or 37-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 (204, 234, 6561)-net over F₂	[i]		Net Duplication
2	Digital (205, 235, 6561)-net over F₂	[i]
3	Digital (206, 236, 6561)-net over F₂	[i]