Best Known (27, 27+11, s)-Nets in Base 81
(27, 27+11, 109528)-Net over F81 — Constructive and digital
Digital (27, 38, 109528)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 3240)-net over F81, using
- net defined by OOA [i] based on linear OOA(817, 3240, F81, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(817, 3240, F81, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- appending kth column [i] based on linear OOA(817, 3240, F81, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(817, 3240, F81, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
- digital (20, 31, 106288)-net over F81, using
- net defined by OOA [i] based on linear OOA(8131, 106288, F81, 11, 11) (dual of [(106288, 11), 1169137, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using
- net defined by OOA [i] based on linear OOA(8131, 106288, F81, 11, 11) (dual of [(106288, 11), 1169137, 12]-NRT-code), using
- digital (2, 7, 3240)-net over F81, using
(27, 27+11, 1011886)-Net over F81 — Digital
Digital (27, 38, 1011886)-net over F81, using
(27, 27+11, large)-Net in Base 81 — Upper bound on s
There is no (27, 38, large)-net in base 81, because
- 9 times m-reduction [i] would yield (27, 29, large)-net in base 81, but