Best Known (29, 29+8, s)-Nets in Base 81
(29, 29+8, 2103792)-Net over F81 — Constructive and digital
Digital (29, 37, 2103792)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (4, 8, 6642)-net over F81, using
- net defined by OOA [i] based on linear OOA(818, 6642, F81, 4, 4) (dual of [(6642, 4), 26560, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(818, 6642, F81, 3, 4) (dual of [(6642, 3), 19918, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(810, s, F81, 3, 0) with arbitrarily large s, using
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(811, 82, F81, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) with arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) with arbitrarily large s, using
- linear OOA(811, 82, F81, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
- linear OOA(812, 82, F81, 3, 2) (dual of [(82, 3), 244, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;244,81) [i]
- linear OOA(814, 82, F81, 3, 4) (dual of [(82, 3), 242, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;242,81) [i]
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(818, 6642, F81, 3, 4) (dual of [(6642, 3), 19918, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(818, 6642, F81, 4, 4) (dual of [(6642, 4), 26560, 5]-NRT-code), using
- digital (21, 29, 2097150)-net over F81, using
- net defined by OOA [i] based on linear OOA(8129, 2097150, F81, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(8129, 8388600, F81, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(8129, 8388600, F81, 8) (dual of [8388600, 8388571, 9]-code), using
- net defined by OOA [i] based on linear OOA(8129, 2097150, F81, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- digital (4, 8, 6642)-net over F81, using
(29, 29+8, large)-Net over F81 — Digital
Digital (29, 37, large)-net over F81, using
- t-expansion [i] based on digital (27, 37, large)-net over F81, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
(29, 29+8, large)-Net in Base 81 — Upper bound on s
There is no (29, 37, large)-net in base 81, because
- 6 times m-reduction [i] would yield (29, 31, large)-net in base 81, but