Best Known (47−22, 47, s)-Nets in Base 27
(47−22, 47, 164)-Net over F27 — Constructive and digital
Digital (25, 47, 164)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (7, 29, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 18, 82)-net over F27, using
(47−22, 47, 224)-Net in Base 27 — Constructive
(25, 47, 224)-net in base 27, using
- 1 times m-reduction [i] based on (25, 48, 224)-net in base 27, using
- base change [i] based on digital (13, 36, 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
- base change [i] based on digital (13, 36, 224)-net over F81, using
(47−22, 47, 617)-Net over F27 — Digital
Digital (25, 47, 617)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2747, 617, F27, 22) (dual of [617, 570, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2747, 743, F27, 22) (dual of [743, 696, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(2743, 729, F27, 22) (dual of [729, 686, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2733, 729, F27, 17) (dual of [729, 696, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(274, 14, F27, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(2747, 743, F27, 22) (dual of [743, 696, 23]-code), using
(47−22, 47, 246523)-Net in Base 27 — Upper bound on s
There is no (25, 47, 246524)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 18 797818 945308 119037 184847 731262 955519 478165 659831 101194 542311 191665 > 2747 [i]