Best Known (195, 195+18, s)-Nets in Base 3
(195, 195+18, 932211)-Net over F3 — Constructive and digital
Digital (195, 213, 932211)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (24, 33, 144)-net over F3, using
- trace code for nets [i] based on digital (2, 11, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- trace code for nets [i] based on digital (2, 11, 48)-net over F27, using
- digital (162, 180, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- digital (24, 33, 144)-net over F3, using
(195, 195+18, 7134515)-Net over F3 — Digital
Digital (195, 213, 7134515)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3213, 7134515, F3, 18) (dual of [7134515, 7134302, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3213, large, F3, 18) (dual of [large, large−213, 19]-code), using
- 33 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 33 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3213, large, F3, 18) (dual of [large, large−213, 19]-code), using
(195, 195+18, large)-Net in Base 3 — Upper bound on s
There is no (195, 213, large)-net in base 3, because
- 16 times m-reduction [i] would yield (195, 197, large)-net in base 3, but