MinT - Information on Result #1228143

Information on Result #1228143

Digital (18, 30, 2881)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (1, 7, 150)-net over F₁₂₈, using
- net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]
digital (11, 23, 2731)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128²³, 2731, F₁₂₈, 12, 12) (dual of [(2731, 12), 32749, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(128²³, 16386, F₁₂₈, 12) (dual of [16386, 16363, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(128²³, 16384, F₁₂₈, 12) (dual of [16384, 16361, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(128²¹, 16384, F₁₂₈, 11) (dual of [16384, 16363, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 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	Digital (19, 31, 2881)-net over F₁₂₈	[i]		Net Duplication