Best Known (146, 146+14, s)-Nets in Base 3
(146, 146+14, 1198485)-Net over F3 — Constructive and digital
Digital (146, 160, 1198485)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (17, 24, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 8, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 8, 38)-net over F27, using
- digital (122, 136, 1198371)-net over F3, using
- net defined by OOA [i] based on linear OOA(3136, 1198371, F3, 14, 14) (dual of [(1198371, 14), 16777058, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3136, 8388597, F3, 14) (dual of [8388597, 8388461, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3136, 8388597, F3, 14) (dual of [8388597, 8388461, 15]-code), using
- net defined by OOA [i] based on linear OOA(3136, 1198371, F3, 14, 14) (dual of [(1198371, 14), 16777058, 15]-NRT-code), using
- digital (17, 24, 114)-net over F3, using
(146, 146+14, 5548648)-Net over F3 — Digital
Digital (146, 160, 5548648)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3160, 5548648, F3, 14) (dual of [5548648, 5548488, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3160, large, F3, 14) (dual of [large, large−160, 15]-code), using
- 24 times code embedding in larger space [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 24 times code embedding in larger space [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3160, large, F3, 14) (dual of [large, large−160, 15]-code), using
(146, 146+14, large)-Net in Base 3 — Upper bound on s
There is no (146, 160, large)-net in base 3, because
- 12 times m-reduction [i] would yield (146, 148, large)-net in base 3, but