Best Known (79−17, 79, s)-Nets in Base 27
(79−17, 79, 66514)-Net over F27 — Constructive and digital
Digital (62, 79, 66514)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 84)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- digital (0, 4, 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, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- generalized (u, u+v)-construction [i] based on
- digital (48, 65, 66430)-net over F27, using
- net defined by OOA [i] based on linear OOA(2765, 66430, F27, 17, 17) (dual of [(66430, 17), 1129245, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2765, 531441, F27, 17) (dual of [531441, 531376, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, 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(2765, 531441, F27, 17) (dual of [531441, 531376, 18]-code), using
- net defined by OOA [i] based on linear OOA(2765, 66430, F27, 17, 17) (dual of [(66430, 17), 1129245, 18]-NRT-code), using
- digital (6, 14, 84)-net over F27, using
(79−17, 79, 66546)-Net in Base 27 — Constructive
(62, 79, 66546)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 14, 116)-net in base 27, using
- 2 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- 2 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- digital (48, 65, 66430)-net over F27, using
- net defined by OOA [i] based on linear OOA(2765, 66430, F27, 17, 17) (dual of [(66430, 17), 1129245, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2765, 531441, F27, 17) (dual of [531441, 531376, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, 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(2765, 531441, F27, 17) (dual of [531441, 531376, 18]-code), using
- net defined by OOA [i] based on linear OOA(2765, 66430, F27, 17, 17) (dual of [(66430, 17), 1129245, 18]-NRT-code), using
- (6, 14, 116)-net in base 27, using
(79−17, 79, 3054394)-Net over F27 — Digital
Digital (62, 79, 3054394)-net over F27, using
(79−17, 79, large)-Net in Base 27 — Upper bound on s
There is no (62, 79, large)-net in base 27, because
- 15 times m-reduction [i] would yield (62, 64, large)-net in base 27, but