Best Known (94, 94+11, s)-Nets in Base 9
(94, 94+11, 3413769)-Net over F9 — Constructive and digital
Digital (94, 105, 3413769)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (18, 23, 58329)-net over F9, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 6481)-net over F9, using
- s-reduction based on digital (0, 0, s)-net over F9 with arbitrarily large s, using
- digital (0, 0, 6481)-net over F9 (see above)
- digital (0, 0, 6481)-net over F9 (see above)
- digital (0, 0, 6481)-net over F9 (see above)
- digital (0, 1, 6481)-net over F9, using
- s-reduction based on digital (0, 1, s)-net over F9 with arbitrarily large s, using
- digital (0, 1, 6481)-net over F9 (see above)
- digital (0, 1, 6481)-net over F9 (see above)
- digital (3, 5, 6481)-net over F9, using
- s-reduction based on digital (3, 5, 7381)-net over F9, using
- digital (10, 15, 6481)-net over F9, using
- net defined by OOA [i] based on linear OOA(915, 6481, F9, 5, 5) (dual of [(6481, 5), 32390, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(915, 12963, F9, 5) (dual of [12963, 12948, 6]-code), using
- 1 times code embedding in larger space [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
- 1 times code embedding in larger space [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(915, 12963, F9, 5) (dual of [12963, 12948, 6]-code), using
- net defined by OOA [i] based on linear OOA(915, 6481, F9, 5, 5) (dual of [(6481, 5), 32390, 6]-NRT-code), using
- digital (0, 0, 6481)-net over F9, using
- generalized (u, u+v)-construction [i] based on
- 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 (18, 23, 58329)-net over F9, using
(94, 94+11, large)-Net over F9 — Digital
Digital (94, 105, large)-net over F9, using
- 91 times duplication [i] based on digital (93, 104, large)-net over F9, using
- t-expansion [i] based on digital (89, 104, large)-net over F9, using
(94, 94+11, large)-Net in Base 9 — Upper bound on s
There is no (94, 105, large)-net in base 9, because
- 9 times m-reduction [i] would yield (94, 96, large)-net in base 9, but