MinT - Information on Result #3222172

Information on Result #3222172

Digital (31, 34, large)-net over F₅, using t-expansion based on digital (30, 34, large)-net over F₅, using

net defined by OOA [i] based on linear OOA(5³⁴, large, F₅, 4, 4), using
- appending kth column [i] based on linear OOA(5³⁴, large, F₅, 3, 4), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(5², 6, F₅, 3, 2) (dual of [(6, 3), 16, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;16,5) [i]
    2. linear OOA(5³², 8388601, F₅, 3, 4) (dual of [(8388601, 3), 25165771, 5]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(5³², 8388602, F₅, 2, 4) (dual of [(8388602, 2), 16777172, 5]-NRT-code), using
        trace code [i] based on linear OOA(25¹⁶, 4194301, F₂₅, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
        OOA 2-folding [i] based on linear OA(25¹⁶, 8388602, F₂₅, 4) (dual of [8388602, 8388586, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹⁶, large, F₂₅, 4) (dual of [large, large−16, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (32, 35, large)-net over F₅	[i]		Net Duplication
2	Digital (33, 36, large)-net over F₅	[i]
3	Digital (34, 37, large)-net over F₅	[i]
4	Digital (35, 38, large)-net over F₅	[i]
5	Digital (36, 39, large)-net over F₅	[i]
6	Digital (37, 40, large)-net over F₅	[i]
7	Digital (38, 41, large)-net over F₅	[i]