Best Known (15−8, 15, s)-Nets in Base 49
(15−8, 15, 600)-Net over F49 — Constructive and digital
Digital (7, 15, 600)-net over F49, using
- net defined by OOA [i] based on linear OOA(4915, 600, F49, 8, 8) (dual of [(600, 8), 4785, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4915, 2400, F49, 8) (dual of [2400, 2385, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(4915, 2400, F49, 8) (dual of [2400, 2385, 9]-code), using
(15−8, 15, 1201)-Net over F49 — Digital
Digital (7, 15, 1201)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4915, 1201, F49, 2, 8) (dual of [(1201, 2), 2387, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4915, 2402, F49, 8) (dual of [2402, 2387, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4915, 2403, F49, 8) (dual of [2403, 2388, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4913, 2401, F49, 7) (dual of [2401, 2388, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(4915, 2403, F49, 8) (dual of [2403, 2388, 9]-code), using
- OOA 2-folding [i] based on linear OA(4915, 2402, F49, 8) (dual of [2402, 2387, 9]-code), using
(15−8, 15, 100470)-Net in Base 49 — Upper bound on s
There is no (7, 15, 100471)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 22 539484 718014 464027 750721 > 4915 [i]