MinT - Information on Result #1191984

Information on Result #1191984

Digital (60, 77, 4099)-net over F₈, using net defined by OOA based on linear OOA(8⁷⁷, 4099, F₈, 17, 17) (dual of [(4099, 17), 69606, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(8⁷⁷, 32793, F₈, 17) (dual of [32793, 32716, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁷⁷, 32794, F₈, 17) (dual of [32794, 32717, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(11) [i] based on
    1. linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(8⁵¹, 32768, F₈, 12) (dual of [32768, 32717, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(8⁶, 26, F₈, 4) (dual of [26, 20, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁶, 56, F₈, 4) (dual of [56, 50, 5]-code), using
        1 times truncation [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
        a code by Danev and Olsson [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		Method
1	Digital (61, 77, 4099)-net over F₈	[i]	t-Expansion
2	Digital (61, 78, 4099)-net over F₈	[i]	Net Duplication
3	Digital (60, 76, 4099)-net over F₈	[i]	m-Reduction