Best Known (29, 29+17, s)-Nets in Base 27
(29, 29+17, 308)-Net over F27 — Constructive and digital
Digital (29, 46, 308)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 28)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 with arbitrarily large s, using
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27, using
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (0, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 5, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 17, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 1, 28)-net over F27, using
(29, 29+17, 820)-Net in Base 27 — Constructive
(29, 46, 820)-net in base 27, using
- 272 times duplication [i] based on (27, 44, 820)-net in base 27, using
- base change [i] based on digital (16, 33, 820)-net over F81, using
- net defined by OOA [i] based on linear OOA(8133, 820, F81, 17, 17) (dual of [(820, 17), 13907, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8133, 6561, F81, 17) (dual of [6561, 6528, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(8133, 6561, F81, 17) (dual of [6561, 6528, 18]-code), using
- net defined by OOA [i] based on linear OOA(8133, 820, F81, 17, 17) (dual of [(820, 17), 13907, 18]-NRT-code), using
- base change [i] based on digital (16, 33, 820)-net over F81, using
(29, 29+17, 3418)-Net over F27 — Digital
Digital (29, 46, 3418)-net over F27, using
(29, 29+17, large)-Net in Base 27 — Upper bound on s
There is no (29, 46, large)-net in base 27, because
- 15 times m-reduction [i] would yield (29, 31, large)-net in base 27, but