MinT - Information on Result #3266944

Information on Result #3266944

Digital (54, 80, 20166)-net over F₆₄, using 64¹ times duplication based on digital (53, 79, 20166)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁷⁹, 20166, F₆₄, 26, 26) (dual of [(20166, 26), 524237, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(64⁷⁹, 262158, F₆₄, 26) (dual of [262158, 262079, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁷⁹, 262159, F₆₄, 26) (dual of [262159, 262080, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
      1. linear OA(64⁷⁶, 262144, F₆₄, 26) (dual of [262144, 262068, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(64⁶⁴, 262144, F₆₄, 22) (dual of [262144, 262080, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(64³, 15, F₆₄, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
        discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [i]

Mode: Constructive and 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

The following results depend on this result:

	Result		This result only	Method
1	(70, 96, 20166)-net in base 32	[i]		Base Change
2	(94, 120, 20166)-net in base 16	[i]		Base Change