Best Known (121−23, 121, s)-Nets in Base 9
(121−23, 121, 48313)-Net over F9 — Constructive and digital
Digital (98, 121, 48313)-net over F9, using
- net defined by OOA [i] based on linear OOA(9121, 48313, F9, 23, 23) (dual of [(48313, 23), 1111078, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9121, 531444, F9, 23) (dual of [531444, 531323, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(9121, 531447, F9, 23) (dual of [531447, 531326, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(9121, 531441, F9, 23) (dual of [531441, 531320, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(9121, 531447, F9, 23) (dual of [531447, 531326, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9121, 531444, F9, 23) (dual of [531444, 531323, 24]-code), using
(121−23, 121, 307751)-Net over F9 — Digital
Digital (98, 121, 307751)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9121, 307751, F9, 23) (dual of [307751, 307630, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(9121, 531441, F9, 23) (dual of [531441, 531320, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(9121, 531441, F9, 23) (dual of [531441, 531320, 24]-code), using
(121−23, 121, large)-Net in Base 9 — Upper bound on s
There is no (98, 121, large)-net in base 9, because
- 21 times m-reduction [i] would yield (98, 100, large)-net in base 9, but