MinT - Information on Result #1708642

Information on Result #1708642

Digital (149, 161, 2796328)-net over F₂, using net defined by OOA based on linear OOA(2¹⁶¹, 2796328, F₂, 18, 12) (dual of [(2796328, 18), 50333743, 13]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁶¹, 2796329, F₂, 6, 12) (dual of [(2796329, 6), 16777813, 13]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁶¹, 2796329, F₂, 3, 12) (dual of [(2796329, 3), 8388826, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²³, 128, F₂, 3, 6) (dual of [(128, 3), 361, 7]-NRT-code), using
      - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²³, 128, F₂, 2, 6) (dual of [(128, 2), 233, 7]-NRT-code), using
        1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹, 127, F₂, 2, 6) (dual of [(127, 2), 233, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2¹³⁸, 2796201, F₂, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: 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

None.