Best Known (219−18, 219, s)-Nets in Base 3
(219−18, 219, 932395)-Net over F3 — Constructive and digital
Digital (201, 219, 932395)-net over F3, using
- 1 times m-reduction [i] based on digital (201, 220, 932395)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (27, 36, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 9, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction 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]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 9, 82)-net over F81, using
- digital (165, 184, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3184, 932067, F3, 21, 19) (dual of [(932067, 21), 19573223, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3184, 2796202, F3, 3, 19) (dual of [(2796202, 3), 8388422, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 2796201, F3, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 2796201, F3, 3, 19) (dual of [(2796201, 3), 8388422, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3184, 2796202, F3, 3, 19) (dual of [(2796202, 3), 8388422, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3184, 932067, F3, 21, 19) (dual of [(932067, 21), 19573223, 20]-NRT-code), using
- digital (27, 36, 328)-net over F3, using
- (u, u+v)-construction [i] based on
(219−18, 219, large)-Net over F3 — Digital
Digital (201, 219, large)-net over F3, using
- 33 times duplication [i] based on digital (198, 216, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3216, large, F3, 18) (dual of [large, large−216, 19]-code), using
- 36 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]
- 36 times code embedding in larger space [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3216, large, F3, 18) (dual of [large, large−216, 19]-code), using
(219−18, 219, large)-Net in Base 3 — Upper bound on s
There is no (201, 219, large)-net in base 3, because
- 16 times m-reduction [i] would yield (201, 203, large)-net in base 3, but