Best Known (48, 48+29, s)-Nets in Base 27
(48, 48+29, 268)-Net over F27 — Constructive and digital
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
(48, 48+29, 468)-Net in Base 27 — Constructive
(48, 77, 468)-net in base 27, using
- 271 times duplication [i] based on (47, 76, 468)-net in base 27, using
- base change [i] based on digital (28, 57, 468)-net over F81, using
- net defined by OOA [i] based on linear OOA(8157, 468, F81, 29, 29) (dual of [(468, 29), 13515, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8157, 6553, F81, 29) (dual of [6553, 6496, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, 6561, F81, 29) (dual of [6561, 6504, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(8157, 6561, F81, 29) (dual of [6561, 6504, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8157, 6553, F81, 29) (dual of [6553, 6496, 30]-code), using
- net defined by OOA [i] based on linear OOA(8157, 468, F81, 29, 29) (dual of [(468, 29), 13515, 30]-NRT-code), using
- base change [i] based on digital (28, 57, 468)-net over F81, using
(48, 48+29, 3766)-Net over F27 — Digital
Digital (48, 77, 3766)-net over F27, using
(48, 48+29, large)-Net in Base 27 — Upper bound on s
There is no (48, 77, large)-net in base 27, because
- 27 times m-reduction [i] would yield (48, 50, large)-net in base 27, but