MinT - Information on Result #1221002

Information on Result #1221002

Digital (72, 82, 3371738)-net over F₂₅, using (u,Â u+v)-construction based on

digital (16, 21, 4194301)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25²¹, 4194301, F₂₅, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(25²¹, large, F₂₅, 5) (dual of [large, large−21, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (51, 61, 1685869)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 15, 8149)-net over F₂₅, using
    - net defined by OOA [i] based on linear OOA(25¹⁵, 8149, F₂₅, 6, 5) (dual of [(8149, 6), 48879, 6]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(25¹⁵, 8150, F₂₅, 2, 5) (dual of [(8150, 2), 16285, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(25⁰, s, F₂₅, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25⁰, 326, F₂₅, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
        linear OOA(25¹, 326, F₂₅, 2, 1) (dual of [(326, 2), 651, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(25¹, s, F₂₅, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(25¹, 326, F₂₅, 2, 1) (dual of [(326, 2), 651, 2]-NRT-code) (see above)
        linear OOA(25¹, 326, F₂₅, 2, 1) (dual of [(326, 2), 651, 2]-NRT-code) (see above)
        linear OOA(25³, 326, F₂₅, 2, 2) (dual of [(326, 2), 649, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(25³, 651, F₂₅, 2, 2) (dual of [(651, 2), 1299, 3]-NRT-code), using
        appending kth column [i] based on linear OA(25³, 651, F₂₅, 2) (dual of [651, 648, 3]-code), using
        Hamming code H(3,25) [i]
        linear OOA(25⁹, 326, F₂₅, 2, 5) (dual of [(326, 2), 643, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(25², 26, F₂₅, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;50,25) [i]
        linear OOA(25⁷, 300, F₂₅, 2, 5) (dual of [(300, 2), 593, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(25⁷, 600, F₂₅, 5) (dual of [600, 593, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]
  2. digital (36, 46, 1677720)-net over F₂₅, using
    - net defined by OOA [i] based on linear OOA(25⁴⁶, 1677720, F₂₅, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
      - OA 5-folding and stacking [i] based on linear OA(25⁴⁶, 8388600, F₂₅, 10) (dual of [8388600, 8388554, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁴⁶, large, F₂₅, 10) (dual of [large, large−46, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (93, 103, 6743476)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets