Best Known (11−6, 11, s)-Nets in Base 49
(11−6, 11, 801)-Net over F49 — Constructive and digital
Digital (5, 11, 801)-net over F49, using
- net defined by OOA [i] based on linear OOA(4911, 801, F49, 6, 6) (dual of [(801, 6), 4795, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(499, 2401, F49, 5) (dual of [2401, 2392, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
(11−6, 11, 1201)-Net over F49 — Digital
Digital (5, 11, 1201)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4911, 1201, F49, 2, 6) (dual of [(1201, 2), 2391, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4911, 2402, F49, 6) (dual of [2402, 2391, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(499, 2401, F49, 5) (dual of [2401, 2392, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
- OOA 2-folding [i] based on linear OA(4911, 2402, F49, 6) (dual of [2402, 2391, 7]-code), using
(11−6, 11, 59637)-Net in Base 49 — Upper bound on s
There is no (5, 11, 59638)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 3 909893 116090 960225 > 4911 [i]