MinT - Information on Result #1179522

Information on Result #1179522

Digital (10, 14, 4098)-net over F₈, using net defined by OOA based on linear OOA(8¹⁴, 4098, F₈, 4, 4) (dual of [(4098, 4), 16378, 5]-NRT-code), using

appending kth column [i] based on linear OOA(8¹⁴, 4098, F₈, 3, 4) (dual of [(4098, 3), 12280, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8¹⁴, 8196, F₈, 4) (dual of [8196, 8182, 5]-code), using
  - trace code [i] based on linear OA(64⁷, 4098, F₆₄, 4) (dual of [4098, 4091, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(64⁷, 4096, F₆₄, 4) (dual of [4096, 4089, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(64⁵, 4096, F₆₄, 3) (dual of [4096, 4091, 4]-code or 4096-cap in PG(4,64)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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.

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 (64, 72, 4198398)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (71, 80, 4198398)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
3	Digital (155, 169, 4797582)-net over F₈	[i]		Generalized (u,Â u+v)-Construction for Nets
4	Digital (140, 153, 5596498)-net over F₈	[i]
5	Digital (133, 145, 5596498)-net over F₈	[i]