Best Known (16−6, 16, s)-Nets in Base 25
(16−6, 16, 5209)-Net over F25 — Constructive and digital
Digital (10, 16, 5209)-net over F25, using
- net defined by OOA [i] based on linear OOA(2516, 5209, F25, 6, 6) (dual of [(5209, 6), 31238, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2516, 15627, F25, 6) (dual of [15627, 15611, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, 15628, F25, 6) (dual of [15628, 15612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2513, 15625, F25, 5) (dual of [15625, 15612, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2516, 15628, F25, 6) (dual of [15628, 15612, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(2516, 15627, F25, 6) (dual of [15627, 15611, 7]-code), using
(16−6, 16, 15628)-Net over F25 — Digital
Digital (10, 16, 15628)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2516, 15628, F25, 6) (dual of [15628, 15612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2513, 15625, F25, 5) (dual of [15625, 15612, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
(16−6, 16, 2161983)-Net in Base 25 — Upper bound on s
There is no (10, 16, 2161984)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 23283 087992 740498 272769 > 2516 [i]