MinT - Information on Result #1208641

Information on Result #1208641

Digital (227, 248, 839024)-net over F₃, using (u,Â u+v)-construction based on

digital (28, 38, 164)-net over F₃, using
- trace code for nets [i] based on digital (9, 19, 82)-net over F₉, using
  - base reduction for projective spaces (embedding PG(9,81) in PG(18,9)) for nets [i] based on digital (0, 10, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
digital (189, 210, 838860)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3²¹⁰, 838860, F₃, 21, 21) (dual of [(838860, 21), 17615850, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(3²¹⁰, 8388601, F₃, 21) (dual of [8388601, 8388391, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (228, 249, 839024)-net over F₃	[i]		Net Duplication