Best Known (10, 10+6, s)-Nets in Base 49
(10, 10+6, 39217)-Net over F49 — Constructive and digital
Digital (10, 16, 39217)-net over F49, using
- net defined by OOA [i] based on linear OOA(4916, 39217, F49, 6, 6) (dual of [(39217, 6), 235286, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(4916, 117651, F49, 6) (dual of [117651, 117635, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4916, 117652, F49, 6) (dual of [117652, 117636, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4913, 117649, F49, 5) (dual of [117649, 117636, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 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(4916, 117652, F49, 6) (dual of [117652, 117636, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(4916, 117651, F49, 6) (dual of [117651, 117635, 7]-code), using
(10, 10+6, 100471)-Net over F49 — Digital
Digital (10, 16, 100471)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4916, 100471, F49, 6) (dual of [100471, 100455, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using
(10, 10+6, large)-Net in Base 49 — Upper bound on s
There is no (10, 16, large)-net in base 49, because
- 4 times m-reduction [i] would yield (10, 12, large)-net in base 49, but