MinT - Information on Result #1191096

Information on Result #1191096

Digital (23, 30, 2796)-net over F₈, using net defined by OOA based on linear OOA(8³⁰, 2796, F₈, 9, 7) (dual of [(2796, 9), 25134, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8³⁰, 2797, F₈, 3, 7) (dual of [(2797, 3), 8361, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁴, 65, F₈, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁴, 65, F₈, 2, 3) (dual of [(65, 2), 126, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
        ovoid in PG(3,Â 8) [i]
  2. linear OOA(8²⁶, 2732, F₈, 3, 7) (dual of [(2732, 3), 8170, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8²⁶, 8196, F₈, 7) (dual of [8196, 8170, 8]-code), using
      - trace code [i] based on linear OA(64¹³, 4098, F₆₄, 7) (dual of [4098, 4085, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(64¹³, 4096, F₆₄, 7) (dual of [4096, 4083, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(64¹¹, 4096, F₆₄, 6) (dual of [4096, 4085, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        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 (122, 136, 2399538)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (129, 144, 2399538)-net over F₈	[i]		(u,Â u+v)-Construction for Nets