Best Known (102, 102+12, s)-Nets in Base 9
(102, 102+12, 2800577)-Net over F9 — Constructive and digital
Digital (102, 114, 2800577)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (18, 24, 4377)-net over F9, using
- net defined by OOA [i] based on linear OOA(924, 4377, F9, 6, 6) (dual of [(4377, 6), 26238, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(924, 13131, F9, 6) (dual of [13131, 13107, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(924, 13132, F9, 6) (dual of [13132, 13108, 7]-code), using
- trace code [i] based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(924, 13132, F9, 6) (dual of [13132, 13108, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(924, 13131, F9, 6) (dual of [13131, 13107, 7]-code), using
- net defined by OOA [i] based on linear OOA(924, 4377, F9, 6, 6) (dual of [(4377, 6), 26238, 7]-NRT-code), using
- digital (78, 90, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- digital (18, 24, 4377)-net over F9, using
(102, 102+12, 2802762)-Net in Base 9 — Constructive
(102, 114, 2802762)-net in base 9, using
- (u, u+v)-construction [i] based on
- (18, 24, 6562)-net in base 9, using
- base change [i] based on digital (10, 16, 6562)-net over F27, using
- net defined by OOA [i] based on linear OOA(2716, 6562, F27, 6, 6) (dual of [(6562, 6), 39356, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2716, 19686, F27, 6) (dual of [19686, 19670, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2716, 19683, F27, 6) (dual of [19683, 19667, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2713, 19683, F27, 5) (dual of [19683, 19670, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(2716, 19686, F27, 6) (dual of [19686, 19670, 7]-code), using
- net defined by OOA [i] based on linear OOA(2716, 6562, F27, 6, 6) (dual of [(6562, 6), 39356, 7]-NRT-code), using
- base change [i] based on digital (10, 16, 6562)-net over F27, using
- digital (78, 90, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- (18, 24, 6562)-net in base 9, using
(102, 102+12, large)-Net over F9 — Digital
Digital (102, 114, large)-net over F9, using
- t-expansion [i] based on digital (101, 114, large)-net over F9, using
- 4 times m-reduction [i] based on digital (101, 118, large)-net over F9, using
(102, 102+12, large)-Net in Base 9 — Upper bound on s
There is no (102, 114, large)-net in base 9, because
- 10 times m-reduction [i] would yield (102, 104, large)-net in base 9, but