MinT - Information on Result #1202328

Information on Result #1202328

Digital (59, 71, 2796250)-net over F₈₁, using net defined by OOA based on linear OOA(81⁷¹, 2796250, F₈₁, 15, 12) (dual of [(2796250, 15), 41943679, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(81⁷¹, 5592501, F₈₁, 3, 12) (dual of [(5592501, 3), 16777432, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁷¹, 5592502, F₈₁, 3, 12) (dual of [(5592502, 3), 16777435, 13]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(81⁵, 100, F₈₁, 3, 4) (dual of [(100, 3), 295, 5]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,295P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
    2. linear OOA(81²¹, 2796201, F₈₁, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OOA(81⁴⁵, 2796201, F₈₁, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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		This result only	Method
1	Digital (130, 142, 5592500)-net over F₉	[i]		Trace Code for Nets