Best Known (27−11, 27, s)-Nets in Base 49
(27−11, 27, 531)-Net over F49 — Constructive and digital
Digital (16, 27, 531)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (10, 21, 480)-net over F49, using
- net defined by OOA [i] based on linear OOA(4921, 480, F49, 11, 11) (dual of [(480, 11), 5259, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using
- net defined by OOA [i] based on linear OOA(4921, 480, F49, 11, 11) (dual of [(480, 11), 5259, 12]-NRT-code), using
- digital (1, 6, 51)-net over F49, using
(27−11, 27, 3554)-Net over F49 — Digital
Digital (16, 27, 3554)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4927, 3554, F49, 11) (dual of [3554, 3527, 12]-code), using
- 1145 step Varšamov–Edel lengthening with (ri) = (3, 7 times 0, 1, 53 times 0, 1, 268 times 0, 1, 813 times 0) [i] based on linear OA(4921, 2403, F49, 11) (dual of [2403, 2382, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(10) ⊂ Ce(9) [i] based on
- 1145 step Varšamov–Edel lengthening with (ri) = (3, 7 times 0, 1, 53 times 0, 1, 268 times 0, 1, 813 times 0) [i] based on linear OA(4921, 2403, F49, 11) (dual of [2403, 2382, 12]-code), using
(27−11, 27, large)-Net in Base 49 — Upper bound on s
There is no (16, 27, large)-net in base 49, because
- 9 times m-reduction [i] would yield (16, 18, large)-net in base 49, but