MinT - Information on Result #1824548

Information on Result #1824548

(40, 56, 262145)-net in base 64, using base change based on digital (32, 48, 262145)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁴⁸, 262145, F₁₂₈, 16, 16) (dual of [(262145, 16), 4194272, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(128⁴⁸, 2097160, F₁₂₈, 16) (dual of [2097160, 2097112, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁸, 2097163, F₁₂₈, 16) (dual of [2097163, 2097115, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
      1. linear OA(128⁴⁶, 2097152, F₁₂₈, 16) (dual of [2097152, 2097106, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(128³⁷, 2097152, F₁₂₈, 13) (dual of [2097152, 2097115, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(128², 11, F₁₂₈, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
        discarding factors / shortening the dual code based on linear OA(128², 128, F₁₂₈, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
        Reedâ€“Solomon code RS(126,128) [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	(41, 57, 262145)-net in base 64	[i]		Net Duplication
2	(42, 58, 262145)-net in base 64	[i]		Net Duplication