Best Known (30, 30+11, s)-Nets in Base 49
(30, 30+11, 1152960)-Net over F49 — Constructive and digital
Digital (30, 41, 1152960)-net over F49, using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, 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(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
(30, 30+11, 2882402)-Net over F49 — Digital
Digital (30, 41, 2882402)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4941, 2882402, F49, 2, 11) (dual of [(2882402, 2), 5764763, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4941, 5764804, F49, 11) (dual of [5764804, 5764763, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4941, 5764805, F49, 11) (dual of [5764805, 5764764, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 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
- discarding factors / shortening the dual code based on linear OA(4941, 5764805, F49, 11) (dual of [5764805, 5764764, 12]-code), using
- OOA 2-folding [i] based on linear OA(4941, 5764804, F49, 11) (dual of [5764804, 5764763, 12]-code), using
(30, 30+11, large)-Net in Base 49 — Upper bound on s
There is no (30, 41, large)-net in base 49, because
- 9 times m-reduction [i] would yield (30, 32, large)-net in base 49, but