Best Known (73, 93, s)-Nets in Base 9
(73, 93, 5908)-Net over F9 — Constructive and digital
Digital (73, 93, 5908)-net over F9, using
- net defined by OOA [i] based on linear OOA(993, 5908, F9, 20, 20) (dual of [(5908, 20), 118067, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(993, 59080, F9, 20) (dual of [59080, 58987, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(993, 59081, F9, 20) (dual of [59081, 58988, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(986, 59049, F9, 20) (dual of [59049, 58963, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(993, 59081, F9, 20) (dual of [59081, 58988, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(993, 59080, F9, 20) (dual of [59080, 58987, 21]-code), using
(73, 93, 59081)-Net over F9 — Digital
Digital (73, 93, 59081)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(993, 59081, F9, 20) (dual of [59081, 58988, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(986, 59049, F9, 20) (dual of [59049, 58963, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(19) ⊂ Ce(13) [i] based on
(73, 93, large)-Net in Base 9 — Upper bound on s
There is no (73, 93, large)-net in base 9, because
- 18 times m-reduction [i] would yield (73, 75, large)-net in base 9, but