MinT - Information on Result #1201996

Information on Result #1201996

Digital (22, 28, 5592401)-net over F₈₁, using net defined by OOA based on linear OOA(81²⁸, 5592401, F₈₁, 9, 6) (dual of [(5592401, 9), 50331581, 7]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(81²⁸, 5592402, F₈₁, 3, 6) (dual of [(5592402, 3), 16777178, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁷, large, F₈₁, 3, 3), using
    - appending kth column [i] based on linear OOA(81⁷, large, F₈₁, 2, 3), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁷, large, F₈₁, 3) (dual of [large, large−7, 4]-code), using
        product of projective cap with 81²-ovoid cap in AG(3,Â 81) [i] based on linear OA(81⁴, 6562, F₈₁, 3) (dual of [6562, 6558, 4]-code or 6562-cap in PG(3,81)), using
        ovoid in PG(3,Â 81) [i]
  2. linear OOA(81²¹, 2796201, F₈₁, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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 (50, 56, large)-net over F₉	[i]		Trace Code for Nets