Best Known (177−16, 177, s)-Nets in Base 3
(177−16, 177, 1048659)-Net over F3 — Constructive and digital
Digital (161, 177, 1048659)-net over F3, using
- 32 times duplication [i] based on digital (159, 175, 1048659)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (16, 24, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 8, 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, 8, 28)-net over F27, using
- digital (135, 151, 1048575)-net over F3, using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- digital (16, 24, 84)-net over F3, using
- (u, u+v)-construction [i] based on
(177−16, 177, 4194442)-Net over F3 — Digital
Digital (161, 177, 4194442)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3177, 4194442, F3, 2, 16) (dual of [(4194442, 2), 8388707, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(326, 141, F3, 2, 8) (dual of [(141, 2), 256, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(326, 141, F3, 8) (dual of [141, 115, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(326, 141, F3, 8) (dual of [141, 115, 9]-code), using
- linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- linear OOA(326, 141, F3, 2, 8) (dual of [(141, 2), 256, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(177−16, 177, large)-Net in Base 3 — Upper bound on s
There is no (161, 177, large)-net in base 3, because
- 14 times m-reduction [i] would yield (161, 163, large)-net in base 3, but