Best Known (74, 74+20, s)-Nets in Base 9
(74, 74+20, 5908)-Net over F9 — Constructive and digital
Digital (74, 94, 5908)-net over F9, using
- 91 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(993, 5908, F9, 20, 20) (dual of [(5908, 20), 118067, 21]-NRT-code), using
(74, 74+20, 59083)-Net over F9 — Digital
Digital (74, 94, 59083)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(994, 59083, F9, 20) (dual of [59083, 58989, 21]-code), using
- construction X with 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
- linear OA(993, 59082, F9, 19) (dual of [59082, 58989, 20]-code), using Gilbert–Varšamov bound and bm = 993 > Vbs−1(k−1) = 215 889528 241362 980167 966869 989370 080376 446716 036631 951717 547879 540453 103251 481741 614921 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 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
- linear OA(993, 59081, F9, 20) (dual of [59081, 58988, 21]-code), using
- construction X with Varšamov bound [i] based on
(74, 74+20, large)-Net in Base 9 — Upper bound on s
There is no (74, 94, large)-net in base 9, because
- 18 times m-reduction [i] would yield (74, 76, large)-net in base 9, but