MinT - Information on Result #1224766

Information on Result #1224766

Digital (99, 110, large)-net over F₃₂, using (u,Â u+v)-construction based on

digital (16, 21, 4194301)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32²¹, 4194301, F₃₂, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(32²¹, large, F₃₂, 5) (dual of [large, large−21, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (78, 89, 4404018)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (16, 21, 4194301)-net over F₃₂ (see above)
  2. digital (57, 68, 2202009)-net over F₃₂, using
    - (u,Â u+v)-construction [i] based on
      1. digital (12, 17, 524289)-net over F₃₂, using
        net defined by OOA [i] based on linear OOA(32¹⁷, 524289, F₃₂, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(32¹⁷, 1048579, F₃₂, 5) (dual of [1048579, 1048562, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹⁷, 1048580, F₃₂, 5) (dual of [1048580, 1048563, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
      2. digital (40, 51, 1677720)-net over F₃₂, using
        net defined by OOA [i] based on linear OOA(32⁵¹, 1677720, F₃₂, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
        OOA 5-folding and stacking with additional row [i] based on linear OA(32⁵¹, 8388601, F₃₂, 11) (dual of [8388601, 8388550, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁵¹, large, F₃₂, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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		Method
1	Digital (100, 110, large)-net over F₃₂	[i]	t-Expansion
2	Digital (101, 110, large)-net over F₃₂	[i]
3	Digital (102, 110, large)-net over F₃₂	[i]
4	Digital (103, 110, large)-net over F₃₂	[i]
5	Digital (104, 110, large)-net over F₃₂	[i]
6	Digital (105, 110, large)-net over F₃₂	[i]
7	Digital (106, 110, large)-net over F₃₂	[i]
8	Digital (107, 110, large)-net over F₃₂	[i]
9	Digital (99, 109, large)-net over F₃₂	[i]	m-Reduction
10	Digital (99, 108, large)-net over F₃₂	[i]
11	Digital (99, 107, large)-net over F₃₂	[i]
12	Digital (99, 106, large)-net over F₃₂	[i]
13	Digital (99, 105, large)-net over F₃₂	[i]
14	Digital (99, 104, large)-net over F₃₂	[i]
15	Digital (99, 103, large)-net over F₃₂	[i]
16	Digital (99, 102, large)-net over F₃₂	[i]