MinT - Information on Result #1824578

Information on Result #1824578

(56, 77, 209717)-net in base 64, using base change based on digital (45, 66, 209717)-net over F₁₂₈, using

128¹ times duplication [i] based on digital (44, 65, 209717)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁶⁵, 209717, F₁₂₈, 21, 21) (dual of [(209717, 21), 4403992, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(128⁶⁵, 2097171, F₁₂₈, 21) (dual of [2097171, 2097106, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(15) [i] based on
      1. linear OA(128⁶¹, 2097152, F₁₂₈, 21) (dual of [2097152, 2097091, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. 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]
      3. linear OA(128⁴, 19, F₁₂₈, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁴, 128, F₁₂₈, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
        Reedâ€“Solomon code RS(124,128) [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	(57, 78, 209717)-net in base 64	[i]		Net Duplication
2	(58, 79, 209717)-net in base 64	[i]		Net Duplication