Best Known (88−18, 88, s)-Nets in Base 9
(88−18, 88, 6565)-Net over F9 — Constructive and digital
Digital (70, 88, 6565)-net over F9, using
- net defined by OOA [i] based on linear OOA(988, 6565, F9, 18, 18) (dual of [(6565, 18), 118082, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(988, 59085, F9, 18) (dual of [59085, 58997, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(988, 59086, F9, 18) (dual of [59086, 58998, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [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(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 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(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(988, 59086, F9, 18) (dual of [59086, 58998, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(988, 59085, F9, 18) (dual of [59085, 58997, 19]-code), using
(88−18, 88, 78075)-Net over F9 — Digital
Digital (70, 88, 78075)-net over F9, using
(88−18, 88, large)-Net in Base 9 — Upper bound on s
There is no (70, 88, large)-net in base 9, because
- 16 times m-reduction [i] would yield (70, 72, large)-net in base 9, but