MinT - Information on Result #1202106

Information on Result #1202106

Digital (6, 15, 199)-net over F₈₁, using net defined by OOA based on linear OOA(81¹⁵, 199, F₈₁, 12, 9) (dual of [(199, 12), 2373, 10]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(81¹⁵, 200, F₈₁, 4, 9) (dual of [(200, 4), 785, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁵, 100, F₈₁, 4, 4) (dual of [(100, 4), 395, 5]-NRT-code), using
    - appending kth column [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]
  2. linear OOA(81¹⁰, 100, F₈₁, 4, 9) (dual of [(100, 4), 390, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,390P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100 (see above)

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	Digital (21, 30, 398)-net over F₉	[i]		Trace Code for Nets