MinT - Information on Result #1198358

Information on Result #1198358

Digital (52, 75, 1792)-net over F₂₇, using net defined by OOA based on linear OOA(27⁷⁵, 1792, F₂₇, 23, 23) (dual of [(1792, 23), 41141, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(27⁷⁵, 19713, F₂₇, 23) (dual of [19713, 19638, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁷⁵, 19716, F₂₇, 23) (dual of [19716, 19641, 24]-code), using
  - constructionÂ X applied to C([0,11]) âŠ‚ C([0,7]) [i] based on
    1. linear OA(27⁶⁷, 19684, F₂₇, 23) (dual of [19684, 19617, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 27⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
    2. linear OA(27⁴³, 19684, F₂₇, 15) (dual of [19684, 19641, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 27⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    3. linear OA(27⁸, 32, F₂₇, 7) (dual of [32, 24, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁸, 38, F₂₇, 7) (dual of [38, 30, 8]-code), using
        extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [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		Method
1	Digital (53, 76, 1792)-net over F₂₇	[i]	Net Duplication
2	Digital (54, 77, 1792)-net over F₂₇	[i]	Net Duplication
3	Digital (52, 74, 1792)-net over F₂₇	[i]	m-Reduction