Best Known (88, 88+11, s)-Nets in Base 9
(88, 88+11, 3362011)-Net over F9 — Constructive and digital
Digital (88, 99, 3362011)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (12, 17, 6571)-net over F9, using
- net defined by OOA [i] based on linear OOA(917, 6571, F9, 6, 5) (dual of [(6571, 6), 39409, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(917, 6572, F9, 2, 5) (dual of [(6572, 2), 13127, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- Hamming code H(3,9) [i]
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- linear OOA(914, 6481, F9, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- trace code [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- OOA 2-folding [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(917, 6572, F9, 2, 5) (dual of [(6572, 2), 13127, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(917, 6571, F9, 6, 5) (dual of [(6571, 6), 39409, 6]-NRT-code), using
- digital (71, 82, 3355440)-net over F9, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- digital (12, 17, 6571)-net over F9, using
(88, 88+11, large)-Net over F9 — Digital
Digital (88, 99, large)-net over F9, using
- 92 times duplication [i] based on digital (86, 97, large)-net over F9, using
- t-expansion [i] based on digital (83, 97, large)-net over F9, using
(88, 88+11, large)-Net in Base 9 — Upper bound on s
There is no (88, 99, large)-net in base 9, because
- 9 times m-reduction [i] would yield (88, 90, large)-net in base 9, but