MinT - Information on Result #1202684

Information on Result #1202684

Digital (32, 50, 795)-net over F₈₁, using net defined by OOA based on linear OOA(81⁵⁰, 795, F₈₁, 21, 18) (dual of [(795, 21), 16645, 19]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(81⁵⁰, 2386, F₈₁, 3, 18) (dual of [(2386, 3), 7108, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁵⁰, 2387, F₈₁, 3, 18) (dual of [(2387, 3), 7111, 19]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(81¹⁵, 200, F₈₁, 3, 9) (dual of [(200, 3), 585, 10]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(81⁵, 100, F₈₁, 3, 4) (dual of [(100, 3), 295, 5]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,295P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
        linear OOA(81¹⁰, 100, F₈₁, 3, 9) (dual of [(100, 3), 290, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,290P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100 (see above)
    2. linear OOA(81³⁵, 2187, F₈₁, 3, 18) (dual of [(2187, 3), 6526, 19]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81³⁵, 6561, F₈₁, 18) (dual of [6561, 6526, 19]-code), using
        an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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

None.