Best Known (208−18, 208, s)-Nets in Base 3
(208−18, 208, 932151)-Net over F3 — Constructive and digital
Digital (190, 208, 932151)-net over F3, using
- 31 times duplication [i] based on digital (189, 207, 932151)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (18, 27, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 9, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 9, 28)-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 (18, 27, 84)-net over F3, using
- (u, u+v)-construction [i] based on
(208−18, 208, 5061319)-Net over F3 — Digital
Digital (190, 208, 5061319)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3208, 5061319, F3, 18) (dual of [5061319, 5061111, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, large, F3, 18) (dual of [large, large−208, 19]-code), using
- 28 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]
- 28 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(3208, large, F3, 18) (dual of [large, large−208, 19]-code), using
(208−18, 208, large)-Net in Base 3 — Upper bound on s
There is no (190, 208, large)-net in base 3, because
- 16 times m-reduction [i] would yield (190, 192, large)-net in base 3, but