MinT - Information on Result #1846359

Information on Result #1846359

(29, 36, 131078)-net in base 8, using base change based on digital (20, 27, 131078)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16²⁷, 131078, F₁₆, 7) (dual of [131078, 131051, 8]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(16²⁶, 131076, F₁₆, 7) (dual of [131076, 131050, 8]-code), using
    - trace code [i] based on linear OA(256¹³, 65538, F₂₅₆, 7) (dual of [65538, 65525, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(256¹³, 65536, F₂₅₆, 7) (dual of [65536, 65523, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  2. linear OA(16²⁶, 131077, F₁₆, 6) (dual of [131077, 131051, 7]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16²⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 244826 778925 460333 687782 998016 [i]
  3. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

Mode: Arbitrary.

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	OOA(8³⁶, 131078, S₈, 2, 7)	[i]		Extracting Embedded OOA
2	OOA(8³⁶, 131078, S₈, 3, 7)	[i]		Extracting Embedded OOA