MinT - Information on Result #1846654

Information on Result #1846654

(33, 56, 21037)-net in base 128, using base change based on digital (26, 49, 21037)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(256⁴⁹, 21037, F₂₅₆, 3, 23) (dual of [(21037, 3), 63062, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(256⁴⁹, 21850, F₂₅₆, 3, 23) (dual of [(21850, 3), 65501, 24]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(256⁴⁹, 65550, F₂₅₆, 23) (dual of [65550, 65501, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(17) [i] based on
      1. linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(256³⁵, 65536, F₂₅₆, 18) (dual of [65536, 65501, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
        Reedâ€“Solomon code RS(252,256) [i]

Mode: Arbitrary.

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	(34, 57, 21037)-net in base 128	[i]		Net Duplication
2	OOA(128⁵⁶, 21037, S₁₂₈, 4, 23)	[i]		Extracting Embedded OOA