MinT - Information on Result #1841721

Information on Result #1841721

(11, 18, 21974)-net in base 128, using net defined by OOA based on OOA(128¹⁸, 21974, S₁₂₈, 9, 7), using

OOA stacking with additional row [i] based on OOA(128¹⁸, 21975, S₁₂₈, 3, 7), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128³, 129, F₁₂₈, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;384,128) [i]
  2. OOA(128¹⁵, 21846, S₁₂₈, 3, 7), using
    - OOA 3-folding [i] based on OA(128¹⁵, 65538, S₁₂₈, 7), using
      - discarding parts of the base [i] based on linear OA(256¹³, 65538, F₂₅₆, 7) (dual of [65538, 65525, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(256¹³, 65536, F₂₅₆, 7) (dual of [65536, 65523, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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	(53, 68, 1220345)-net in base 128	[i]		(u,Â u+v)-Construction for Nets