Best Known (185, 227, s)-Nets in Base 3
(185, 227, 896)-Net over F3 — Constructive and digital
Digital (185, 227, 896)-net over F3, using
- t-expansion [i] based on digital (184, 227, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (184, 228, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 57, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 57, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (184, 228, 896)-net over F3, using
(185, 227, 3875)-Net over F3 — Digital
Digital (185, 227, 3875)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3227, 3875, F3, 42) (dual of [3875, 3648, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3227, 6566, F3, 42) (dual of [6566, 6339, 43]-code), using
- construction X applied to C([0,21]) ⊂ C([0,19]) [i] based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3209, 6562, F3, 39) (dual of [6562, 6353, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- construction X applied to C([0,21]) ⊂ C([0,19]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3227, 6566, F3, 42) (dual of [6566, 6339, 43]-code), using
(185, 227, 623593)-Net in Base 3 — Upper bound on s
There is no (185, 227, 623594)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 025472 219145 249159 604448 403943 621723 096216 999426 037709 982092 862281 871888 705447 293508 567340 194140 282749 848717 > 3227 [i]