MinT - Information on Result #1202586

Information on Result #1202586

Digital (57, 73, 1048656)-net over F₈₁, using net defined by OOA based on linear OOA(81⁷³, 1048656, F₈₁, 20, 16) (dual of [(1048656, 20), 20973047, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(81⁷³, 2097313, F₈₁, 4, 16) (dual of [(2097313, 4), 8389179, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁷³, 2097314, F₈₁, 4, 16) (dual of [(2097314, 4), 8389183, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(81¹², 164, F₈₁, 4, 8) (dual of [(164, 4), 644, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(81⁴, 82, F₈₁, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;324,81) [i]
        linear OOA(81⁸, 82, F₈₁, 4, 8) (dual of [(82, 4), 320, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;320,81) [i]
    2. linear OOA(81⁶¹, 2097150, F₈₁, 4, 16) (dual of [(2097150, 4), 8388539, 17]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(81⁶¹, 8388600, F₈₁, 16) (dual of [8388600, 8388539, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁶¹, large, F₈₁, 16) (dual of [large, large−61, 17]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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, 146, 2097312)-net over F₉	[i]		Trace Code for Nets