Best Known (87−18, 87, s)-Nets in Base 9
(87−18, 87, 6564)-Net over F9 — Constructive and digital
Digital (69, 87, 6564)-net over F9, using
- net defined by OOA [i] based on linear OOA(987, 6564, F9, 18, 18) (dual of [(6564, 18), 118065, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(987, 59076, F9, 18) (dual of [59076, 58989, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(987, 59080, F9, 18) (dual of [59080, 58993, 19]-code), using
- 1 times truncation [i] based on linear OA(988, 59081, F9, 19) (dual of [59081, 58993, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(981, 59049, F9, 19) (dual of [59049, 58968, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(97, 32, F9, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(988, 59081, F9, 19) (dual of [59081, 58993, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(987, 59080, F9, 18) (dual of [59080, 58993, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(987, 59076, F9, 18) (dual of [59076, 58989, 19]-code), using
(87−18, 87, 68610)-Net over F9 — Digital
Digital (69, 87, 68610)-net over F9, using
(87−18, 87, large)-Net in Base 9 — Upper bound on s
There is no (69, 87, large)-net in base 9, because
- 16 times m-reduction [i] would yield (69, 71, large)-net in base 9, but