MinT - Information on Result #1824248

Information on Result #1824248

(65, 90, 21846)-net in base 32, using base change based on digital (50, 75, 21846)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁷⁵, 21846, F₆₄, 25, 25) (dual of [(21846, 25), 546075, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(64⁷⁵, 262153, F₆₄, 25) (dual of [262153, 262078, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁷⁵, 262155, F₆₄, 25) (dual of [262155, 262080, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(64⁷³, 262144, F₆₄, 25) (dual of [262144, 262071, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(64², 11, F₆₄, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
        discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [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	(66, 91, 21846)-net in base 32	[i]		Net Duplication
2	(67, 92, 21846)-net in base 32	[i]
3	(68, 93, 21846)-net in base 32	[i]
4	(65, 89, 21846)-net in base 32	[i]		m-Reduction