Best Known (26, 26+6, s)-Nets in Base 9
(26, 26+6, 354296)-Net over F9 — Constructive and digital
Digital (26, 32, 354296)-net over F9, using
- net defined by OOA [i] based on linear OOA(932, 354296, F9, 6, 6) (dual of [(354296, 6), 2125744, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(932, 1062888, F9, 6) (dual of [1062888, 1062856, 7]-code), using
- trace code [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(932, 1062888, F9, 6) (dual of [1062888, 1062856, 7]-code), using
(26, 26+6, 1062888)-Net over F9 — Digital
Digital (26, 32, 1062888)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(932, 1062888, F9, 6) (dual of [1062888, 1062856, 7]-code), using
- trace code [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
(26, 26+6, large)-Net in Base 9 — Upper bound on s
There is no (26, 32, large)-net in base 9, because
- 4 times m-reduction [i] would yield (26, 28, large)-net in base 9, but