Best Known (147−26, 147, s)-Nets in Base 9
(147−26, 147, 40883)-Net over F9 — Constructive and digital
Digital (121, 147, 40883)-net over F9, using
- 91 times duplication [i] based on digital (120, 146, 40883)-net over F9, using
- net defined by OOA [i] based on linear OOA(9146, 40883, F9, 26, 26) (dual of [(40883, 26), 1062812, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9146, 531479, F9, 26) (dual of [531479, 531333, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(97, 43, F9, 5) (dual of [43, 36, 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(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9146, 531479, F9, 26) (dual of [531479, 531333, 27]-code), using
- net defined by OOA [i] based on linear OOA(9146, 40883, F9, 26, 26) (dual of [(40883, 26), 1062812, 27]-NRT-code), using
(147−26, 147, 531486)-Net over F9 — Digital
Digital (121, 147, 531486)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9147, 531486, F9, 26) (dual of [531486, 531339, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(97, 43, F9, 5) (dual of [43, 36, 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(25) ⊂ Ce(19) [i] based on
- linear OA(9146, 531485, F9, 25) (dual of [531485, 531339, 26]-code), using Gilbert–Varšamov bound and bm = 9146 > Vbs−1(k−1) = 1963 340447 370567 399471 134255 106035 220211 318459 137657 091033 264297 084184 510224 851521 731861 716596 177153 632797 751858 386164 785060 425282 029409 [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(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- construction X with Varšamov bound [i] based on
(147−26, 147, large)-Net in Base 9 — Upper bound on s
There is no (121, 147, large)-net in base 9, because
- 24 times m-reduction [i] would yield (121, 123, large)-net in base 9, but