MinT - Information on Result #1203878

Information on Result #1203878

Digital (45, 65, 209718)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁵, 209718, F₁₂₈, 20, 20) (dual of [(209718, 20), 4194295, 21]-NRT-code), using

OA 10-folding and stacking [i] based on linear OA(128⁶⁵, 2097180, F₁₂₈, 20) (dual of [2097180, 2097115, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁶⁵, 2097183, F₁₂₈, 20) (dual of [2097183, 2097118, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(11) [i] based on
    1. linear OA(128⁵⁸, 2097152, F₁₂₈, 20) (dual of [2097152, 2097094, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(128⁷, 31, F₁₂₈, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
        Reedâ€“Solomon code RS(121,128) [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	Digital (46, 66, 209718)-net over F₁₂₈	[i]		Net Duplication
2	(71, 91, 209718)-net in base 32	[i]		Base Change