MinT - Information on Result #3280367

Information on Result #3280367

(55, 85, 4370)-net in base 64, using 64¹ times duplication based on (54, 84, 4370)-net in base 64, using

base change [i] based on digital (33, 63, 4370)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁶³, 4370, F₂₅₆, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
  - OA 15-folding and stacking [i] based on linear OA(256⁶³, 65550, F₂₅₆, 30) (dual of [65550, 65487, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(24) [i] based on
      1. linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
        Reedâ€“Solomon code RS(252,256) [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	(72, 102, 4370)-net in base 32	[i]		Base Change