Best Known (192, 227, s)-Nets in Base 3
(192, 227, 1494)-Net over F3 — Constructive and digital
Digital (192, 227, 1494)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 23, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- digital (169, 204, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 51, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 51, 370)-net over F81, using
- digital (6, 23, 14)-net over F3, using
(192, 227, 12155)-Net over F3 — Digital
Digital (192, 227, 12155)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3227, 12155, F3, 35) (dual of [12155, 11928, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3227, 19747, F3, 35) (dual of [19747, 19520, 36]-code), using
- 4 times code embedding in larger space [i] based on linear OA(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- 4 times code embedding in larger space [i] based on linear OA(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3227, 19747, F3, 35) (dual of [19747, 19520, 36]-code), using
(192, 227, 7903517)-Net in Base 3 — Upper bound on s
There is no (192, 227, 7903518)-net in base 3, because
- 1 times m-reduction [i] would yield (192, 226, 7903518)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 675156 446450 649810 344892 456530 935036 864097 609772 093288 586151 901006 764027 924714 771696 428923 027412 679303 044125 > 3226 [i]