MinT - Information on Result #1842647

Information on Result #1842647

(127, 140, 5592402)-net in base 9, using (u,Â u+v)-construction based on

(33, 39, 2796201)-net in base 9, using
- base change [i] based on digital (20, 26, 2796201)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27²⁶, 2796201, F₂₇, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(27²⁶, large, F₂₇, 6) (dual of [large, large−26, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (88, 101, 2796201)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹⁰¹, 2796201, F₉, 15, 13) (dual of [(2796201, 15), 41942914, 14]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(9¹⁰¹, 5592403, F₉, 3, 13) (dual of [(5592403, 3), 16777108, 14]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(9⁹⁸, 5592402, F₉, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁹, 2796201, F₈₁, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive.

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		This result only	Method
1	(128, 141, 5592402)-net in base 9	[i]		Net Duplication