Best Known (202−19, 202, s)-Nets in Base 3
(202−19, 202, 932098)-Net over F3 — Constructive and digital
Digital (183, 202, 932098)-net over F3, using
- 31 times duplication [i] based on digital (182, 201, 932098)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (11, 20, 32)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- trace code for nets [i] based on digital (1, 10, 16)-net over F9, 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 (11, 20, 32)-net over F3, using
- (u, u+v)-construction [i] based on
(202−19, 202, 3129841)-Net over F3 — Digital
Digital (183, 202, 3129841)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3202, 3129841, F3, 2, 19) (dual of [(3129841, 2), 6259480, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3202, 4194333, F3, 2, 19) (dual of [(4194333, 2), 8388464, 20]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3201, 4194333, F3, 2, 19) (dual of [(4194333, 2), 8388465, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(320, 32, F3, 2, 9) (dual of [(32, 2), 44, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 20, 32)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- trace code for nets [i] based on digital (1, 10, 16)-net over F9, using
- extracting embedded OOA [i] based on digital (11, 20, 32)-net over F3, using
- linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 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 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- linear OOA(320, 32, F3, 2, 9) (dual of [(32, 2), 44, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- 31 times duplication [i] based on linear OOA(3201, 4194333, F3, 2, 19) (dual of [(4194333, 2), 8388465, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3202, 4194333, F3, 2, 19) (dual of [(4194333, 2), 8388464, 20]-NRT-code), using
(202−19, 202, large)-Net in Base 3 — Upper bound on s
There is no (183, 202, large)-net in base 3, because
- 17 times m-reduction [i] would yield (183, 185, large)-net in base 3, but