MinT - Information on Result #1202024

Information on Result #1202024

Digital (15, 22, 177229)-net over F₈₁, using net defined by OOA based on linear OOA(81²², 177229, F₈₁, 9, 7) (dual of [(177229, 9), 1595039, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(81²², 177230, F₈₁, 3, 7) (dual of [(177230, 3), 531668, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81³, 82, F₈₁, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;243,81) [i]
  2. linear OOA(81¹⁹, 177148, F₈₁, 3, 7) (dual of [(177148, 3), 531425, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81¹⁹, 531444, F₈₁, 7) (dual of [531444, 531425, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(81¹⁹, 531441, F₈₁, 7) (dual of [531441, 531422, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(81¹⁶, 531441, F₈₁, 6) (dual of [531441, 531425, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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 (61, 75, 1375600)-net over F₈₁	[i]		(u,Â u+v)-Construction for Nets
2	Digital (64, 79, 1375600)-net over F₈₁	[i]		(u,Â u+v)-Construction for Nets