Best Known (31−5, 31, s)-Nets in Base 9
(31−5, 31, 2391497)-Net over F9 — Constructive and digital
Digital (26, 31, 2391497)-net over F9, using
- net defined by OOA [i] based on linear OOA(931, 2391497, F9, 6, 5) (dual of [(2391497, 6), 14348951, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(931, 2391498, F9, 2, 5) (dual of [(2391498, 2), 4782965, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(92, 10, F9, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;18,9) [i]
- linear OOA(929, 2391488, F9, 2, 5) (dual of [(2391488, 2), 4782947, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(929, 4782976, F9, 5) (dual of [4782976, 4782947, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(929, 4782969, F9, 5) (dual of [4782969, 4782940, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(922, 4782969, F9, 4) (dual of [4782969, 4782947, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(929, 4782976, F9, 5) (dual of [4782976, 4782947, 6]-code), using
- linear OOA(92, 10, F9, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(931, 2391498, F9, 2, 5) (dual of [(2391498, 2), 4782965, 6]-NRT-code), using
(31−5, 31, 6876103)-Net over F9 — Digital
Digital (26, 31, 6876103)-net over F9, using
(31−5, 31, large)-Net in Base 9 — Upper bound on s
There is no (26, 31, large)-net in base 9, because
- 3 times m-reduction [i] would yield (26, 28, large)-net in base 9, but