Best Known (48, 76, s)-Nets in Base 27
(48, 76, 268)-Net over F27 — Constructive and digital
Digital (48, 76, 268)-net over F27, using
- 1 times m-reduction [i] based on digital (48, 77, 268)-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 (6, 35, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 11, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(48, 76, 469)-Net in Base 27 — Constructive
(48, 76, 469)-net in base 27, using
- base change [i] based on digital (29, 57, 469)-net over F81, using
- 1 times m-reduction [i] based on digital (29, 58, 469)-net over F81, using
- net defined by OOA [i] based on linear OOA(8158, 469, F81, 29, 29) (dual of [(469, 29), 13543, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [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
- OOA 14-folding and stacking with additional row [i] based on linear OA(8158, 6567, F81, 29) (dual of [6567, 6509, 30]-code), using
- net defined by OOA [i] based on linear OOA(8158, 469, F81, 29, 29) (dual of [(469, 29), 13543, 30]-NRT-code), using
- 1 times m-reduction [i] based on digital (29, 58, 469)-net over F81, using
(48, 76, 4506)-Net over F27 — Digital
Digital (48, 76, 4506)-net over F27, using
(48, 76, large)-Net in Base 27 — Upper bound on s
There is no (48, 76, large)-net in base 27, because
- 26 times m-reduction [i] would yield (48, 50, large)-net in base 27, but