MinT - Information on Result #1179546

Information on Result #1179546

Digital (24, 28, large)-net over F₈, using net defined by OOA based on linear OOA(8²⁸, large, F₈, 4, 4), using

appending kth column [i] based on linear OOA(8²⁸, large, F₈, 3, 4), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8², 9, F₈, 3, 2) (dual of [(9, 3), 25, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;25,8) [i]
  2. linear OOA(8²⁶, 8388602, F₈, 3, 4) (dual of [(8388602, 3), 25165780, 5]-NRT-code), using
    - trace code [i] based on linear OOA(64¹³, 4194301, F₆₄, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
      - OA 2-folding and stacking [i] based on linear OA(64¹³, 8388602, F₆₄, 4) (dual of [8388602, 8388589, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹³, large, F₆₄, 4) (dual of [large, large−13, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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 (25, 28, large)-net over F₈	[i]		t-Expansion
2	Digital (25, 29, large)-net over F₈	[i]		Net Duplication
3	Digital (26, 30, large)-net over F₈	[i]
4	Digital (27, 31, large)-net over F₈	[i]
5	Digital (28, 32, large)-net over F₈	[i]
6	Digital (29, 33, large)-net over F₈	[i]
7	Digital (30, 34, large)-net over F₈	[i]
8	Digital (24, 27, large)-net over F₈	[i]		m-Reduction