MinT - Information on Result #1824225

Information on Result #1824225

(57, 78, 26216)-net in base 32, using base change based on digital (44, 65, 26216)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁶⁵, 26216, F₆₄, 21, 21) (dual of [(26216, 21), 550471, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(64⁶⁵, 262161, F₆₄, 21) (dual of [262161, 262096, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁶⁵, 262163, F₆₄, 21) (dual of [262163, 262098, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(15) [i] based on
      1. linear OA(64⁶¹, 262144, F₆₄, 21) (dual of [262144, 262083, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(64⁴⁶, 262144, F₆₄, 16) (dual of [262144, 262098, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(64⁴, 19, F₆₄, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
        discarding factors / shortening the dual code based on linear OA(64⁴, 64, F₆₄, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
        Reedâ€“Solomon code RS(60,64) [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	(58, 79, 26216)-net in base 32	[i]		Net Duplication
2	(59, 80, 26216)-net in base 32	[i]		Net Duplication