Best Known (203, 222, s)-Nets in Base 3
(203, 222, 932466)-Net over F3 — Constructive and digital
Digital (203, 222, 932466)-net over F3, using
- 31 times duplication [i] based on digital (202, 221, 932466)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (31, 40, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- digital (162, 181, 932066)-net over F3, using
- net defined by OOA [i] based on linear OOA(3181, 932066, F3, 19, 19) (dual of [(932066, 19), 17709073, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3181, 8388595, F3, 19) (dual of [8388595, 8388414, 20]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3181, 8388595, F3, 19) (dual of [8388595, 8388414, 20]-code), using
- net defined by OOA [i] based on linear OOA(3181, 932066, F3, 19, 19) (dual of [(932066, 19), 17709073, 20]-NRT-code), using
- digital (31, 40, 400)-net over F3, using
- (u, u+v)-construction [i] based on
(203, 222, 5721242)-Net over F3 — Digital
Digital (203, 222, 5721242)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3222, 5721242, F3, 19) (dual of [5721242, 5721020, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, large, F3, 19) (dual of [large, large−222, 20]-code), using
- 41 times code embedding in larger space [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]
- 41 times code embedding in larger space [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, large, F3, 19) (dual of [large, large−222, 20]-code), using
(203, 222, large)-Net in Base 3 — Upper bound on s
There is no (203, 222, large)-net in base 3, because
- 17 times m-reduction [i] would yield (203, 205, large)-net in base 3, but