Best Known (108, 108+25, s)-Nets in Base 9
(108, 108+25, 44287)-Net over F9 — Constructive and digital
Digital (108, 133, 44287)-net over F9, using
- net defined by OOA [i] based on linear OOA(9133, 44287, F9, 25, 25) (dual of [(44287, 25), 1107042, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9133, 531445, F9, 25) (dual of [531445, 531312, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 531447, F9, 25) (dual of [531447, 531314, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(9133, 531441, F9, 25) (dual of [531441, 531308, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 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
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(9133, 531447, F9, 25) (dual of [531447, 531314, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9133, 531445, F9, 25) (dual of [531445, 531312, 26]-code), using
(108, 108+25, 353079)-Net over F9 — Digital
Digital (108, 133, 353079)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9133, 353079, F9, 25) (dual of [353079, 352946, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 531441, F9, 25) (dual of [531441, 531308, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(9133, 531441, F9, 25) (dual of [531441, 531308, 26]-code), using
(108, 108+25, large)-Net in Base 9 — Upper bound on s
There is no (108, 133, large)-net in base 9, because
- 23 times m-reduction [i] would yield (108, 110, large)-net in base 9, but