Best Known (219−20, 219, s)-Nets in Base 3
(219−20, 219, 838892)-Net over F3 — Constructive and digital
Digital (199, 219, 838892)-net over F3, using
- 31 times duplication [i] based on digital (198, 218, 838892)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (12, 22, 32)-net over F3, using
- trace code for nets [i] based on digital (1, 11, 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, 11, 16)-net over F9, using
- digital (176, 196, 838860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3196, 838860, F3, 20, 20) (dual of [(838860, 20), 16777004, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- net defined by OOA [i] based on linear OOA(3196, 838860, F3, 20, 20) (dual of [(838860, 20), 16777004, 21]-NRT-code), using
- digital (12, 22, 32)-net over F3, using
- (u, u+v)-construction [i] based on
(219−20, 219, 4194335)-Net over F3 — Digital
Digital (199, 219, 4194335)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3219, 4194335, F3, 2, 20) (dual of [(4194335, 2), 8388451, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(323, 34, F3, 2, 10) (dual of [(34, 2), 45, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(323, 68, F3, 10) (dual of [68, 45, 11]-code), using
- a “Glo†code from Brouwer’s database [i]
- OOA 2-folding [i] based on linear OA(323, 68, F3, 10) (dual of [68, 45, 11]-code), using
- linear OOA(3196, 4194301, F3, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- linear OOA(323, 34, F3, 2, 10) (dual of [(34, 2), 45, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(219−20, 219, large)-Net in Base 3 — Upper bound on s
There is no (199, 219, large)-net in base 3, because
- 18 times m-reduction [i] would yield (199, 201, large)-net in base 3, but