Best Known (28, 45, s)-Nets in Base 81
(28, 45, 984)-Net over F81 — Constructive and digital
Digital (28, 45, 984)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 164)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 4, 82)-net over F81, using
- (u, u+v)-construction [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
- digital (4, 12, 164)-net over F81, using
(28, 45, 19826)-Net over F81 — Digital
Digital (28, 45, 19826)-net over F81, using
(28, 45, large)-Net in Base 81 — Upper bound on s
There is no (28, 45, large)-net in base 81, because
- 15 times m-reduction [i] would yield (28, 30, large)-net in base 81, but