MinT - Information on Result #3267337

Information on Result #3267337

Digital (58, 81, 48429)-net over F₈₁, using 81¹ times duplication based on digital (57, 80, 48429)-net over F₈₁, using

(u,Â u+v)-construction [i] based on
1. digital (2, 13, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]
2. digital (44, 67, 48313)-net over F₈₁, using
  - net defined by OOA [i] based on linear OOA(81⁶⁷, 48313, F₈₁, 23, 23) (dual of [(48313, 23), 1111132, 24]-NRT-code), using
    - OOA 11-folding and stacking with additional row [i] based on linear OA(81⁶⁷, 531444, F₈₁, 23) (dual of [531444, 531377, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
        linear OA(81⁶⁷, 531441, F₈₁, 23) (dual of [531441, 531374, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(81⁶⁴, 531441, F₈₁, 22) (dual of [531441, 531377, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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	(85, 108, 48429)-net in base 27	[i]		Base Change