MinT - Information on Result #1831573

Information on Result #1831573

OOA(4²³², 4194688, S₄, 2, 22), using (u,Â u+v)-construction based on

OOA(4³⁹, 387, S₄, 2, 11), using
- extracting embedded OOA [i] based on (28, 39, 387)-net in base 4, using
  - trace code for nets [i] based on (2, 13, 129)-net in base 64, using
    - 1 times m-reduction [i] based on (2, 14, 129)-net in base 64, using
      - base change [i] based on digital (0, 12, 129)-net over F₁₂₈, using
        net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
linear OOA(4¹⁹³, 4194301, F₄, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁹³, 8388602, F₄, 22) (dual of [8388602, 8388409, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁹³, large, F₄, 22) (dual of [large, large−193, 23]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

None.

The following results depend on this result:

	Result		This result only	Method
1	OOA(4²³³, 4194688, S₄, 2, 22)	[i]		OOA Duplication