MinT - Information on Result #1191701

Information on Result #1191701

Linear OOA(8¹¹⁵, 2796330, F₈, 15, 13) (dual of [(2796330, 15), 41944835, 14]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(8¹¹⁵, 5592661, F₈, 3, 13) (dual of [(5592661, 3), 16777868, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8¹¹⁵, 5592662, F₈, 3, 13) (dual of [(5592662, 3), 16777871, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹⁷, 260, F₈, 3, 6) (dual of [(260, 3), 763, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
        caps completed using a computer search [i]
      2. linear OOA(8¹², 130, F₈, 3, 6) (dual of [(130, 3), 378, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 12, 130)-net over F₈, using
        trace code for nets [i] based on digital (0, 6, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(8⁹⁸, 5592402, F₈, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
    - trace code [i] based on linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (102, 115, 2796330)-net over F₈	[i]		Net Defined by OOA