MinT - Information on Result #1213187

Information on Result #1213187

Digital (57, 63, 5636278)-net over F₅, using (u,Â u+v)-construction based on

digital (8, 11, 43876)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹¹, 43876, F₅, 3, 3) (dual of [(43876, 3), 131617, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(5¹¹, 43876, F₅, 2, 3) (dual of [(43876, 2), 87741, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹¹, 43876, F₅, 3) (dual of [43876, 43865, 4]-code or 43876-cap in PG(10,5)), using
      - product of projective cap with cap in AG(4,Â 5) [i] based on linear OA(5⁷, 675, F₅, 3) (dual of [675, 668, 4]-code or 675-cap in PG(6,5)), using
        product of two caps with tangent hyperplane [i]
digital (46, 52, 5592402)-net over F₅, using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25²⁶, 2796201, F₂₅, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(25²⁶, large, F₂₅, 6) (dual of [large, large−26, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5⁶³, 5636278, F₅, 3, 6) (dual of [(5636278, 3), 16908771, 7]-NRT-code)	[i]		Extracting Embedded OOA