MinT - Information on Result #3206664

Information on Result #3206664

Digital (101, 104, large)-net over F₄, using t-expansion based on digital (96, 104, large)-net over F₄, using

trace code for nets [i] based on digital (18, 26, 2097406)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256²⁶, 2097406, F₂₅₆, 12, 8) (dual of [(2097406, 12), 25168846, 9]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(256²⁶, 2097407, F₂₅₆, 4, 8) (dual of [(2097407, 4), 8389602, 9]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(256⁴, 257, F₂₅₆, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1024,256) [i]
      2. linear OOA(256²², 2097150, F₂₅₆, 4, 8) (dual of [(2097150, 4), 8388578, 9]-NRT-code), using
        OOA 4-folding [i] based on linear OA(256²², 8388600, F₂₅₆, 8) (dual of [8388600, 8388578, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(256²², large, F₂₅₆, 8) (dual of [large, large−22, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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 (102, 105, large)-net over F₄	[i]		Net Duplication
2	Digital (103, 106, large)-net over F₄	[i]
3	Digital (104, 107, large)-net over F₄	[i]
4	Digital (105, 108, large)-net over F₄	[i]
5	Digital (106, 109, large)-net over F₄	[i]