Best Known (49, 49+28, s)-Nets in Base 27
(49, 49+28, 274)-Net over F27 — Constructive and digital
Digital (49, 77, 274)-net over F27, using
- 1 times m-reduction [i] based on digital (49, 78, 274)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 11, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 18, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (7, 36, 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 (4, 11, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(49, 49+28, 469)-Net in Base 27 — Constructive
(49, 77, 469)-net in base 27, using
- 1 times m-reduction [i] based on (49, 78, 469)-net in base 27, using
- net defined by OOA [i] based on OOA(2778, 469, S27, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(2778, 6567, S27, 29), using
- discarding parts of the base [i] based on linear OA(8158, 6567, F81, 29) (dual of [6567, 6509, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(8157, 6562, F81, 29) (dual of [6562, 6505, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(8153, 6562, F81, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- discarding parts of the base [i] based on linear OA(8158, 6567, F81, 29) (dual of [6567, 6509, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on OA(2778, 6567, S27, 29), using
- net defined by OOA [i] based on OOA(2778, 469, S27, 29, 29), using
(49, 49+28, 5089)-Net over F27 — Digital
Digital (49, 77, 5089)-net over F27, using
(49, 49+28, large)-Net in Base 27 — Upper bound on s
There is no (49, 77, large)-net in base 27, because
- 26 times m-reduction [i] would yield (49, 51, large)-net in base 27, but