Best Known (92, 92+11, s)-Nets in Base 9
(92, 92+11, 3384966)-Net over F9 — Constructive and digital
Digital (92, 103, 3384966)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (16, 21, 29526)-net over F9, using
- net defined by OOA [i] based on linear OOA(921, 29526, F9, 5, 5) (dual of [(29526, 5), 147609, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(921, 59053, F9, 5) (dual of [59053, 59032, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(921, 59054, F9, 5) (dual of [59054, 59033, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(921, 59049, F9, 5) (dual of [59049, 59028, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(916, 59049, F9, 4) (dual of [59049, 59033, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(921, 59054, F9, 5) (dual of [59054, 59033, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(921, 59053, F9, 5) (dual of [59053, 59032, 6]-code), using
- net defined by OOA [i] based on linear OOA(921, 29526, F9, 5, 5) (dual of [(29526, 5), 147609, 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 (16, 21, 29526)-net over F9, using
(92, 92+11, large)-Net over F9 — Digital
Digital (92, 103, large)-net over F9, using
- t-expansion [i] based on digital (89, 103, large)-net over F9, using
- 1 times m-reduction [i] based on digital (89, 104, large)-net over F9, using
(92, 92+11, large)-Net in Base 9 — Upper bound on s
There is no (92, 103, large)-net in base 9, because
- 9 times m-reduction [i] would yield (92, 94, large)-net in base 9, but