Best Known (17, 22, s)-Nets in Base 7
(17, 22, 16470)-Net over F7 — Constructive and digital
Digital (17, 22, 16470)-net over F7, using
- net defined by OOA [i] based on linear OOA(722, 16470, F7, 6, 5) (dual of [(16470, 6), 98798, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(722, 16471, F7, 2, 5) (dual of [(16471, 2), 32920, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(70, 2353, F7, 2, 0) (dual of [(2353, 2), 4706, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(70, s, F7, 2, 0) with arbitrarily large s, using
- linear OOA(70, 2353, F7, 2, 0) (dual of [(2353, 2), 4706, 1]-NRT-code) (see above)
- linear OOA(71, 2353, F7, 2, 1) (dual of [(2353, 2), 4705, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 2, 1) with arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 2, 1) with arbitrarily large s, using
- linear OOA(71, 2353, F7, 2, 1) (dual of [(2353, 2), 4705, 2]-NRT-code) (see above)
- linear OOA(71, 2353, F7, 2, 1) (dual of [(2353, 2), 4705, 2]-NRT-code) (see above)
- linear OOA(75, 2353, F7, 2, 2) (dual of [(2353, 2), 4701, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(75, 2801, F7, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
- appending kth column [i] based on linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- Hamming code H(5,7) [i]
- appending kth column [i] based on linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(75, 2801, F7, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
- linear OOA(714, 2353, F7, 2, 5) (dual of [(2353, 2), 4692, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- trace code [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- OOA 2-folding [i] based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- linear OOA(70, 2353, F7, 2, 0) (dual of [(2353, 2), 4706, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(722, 16471, F7, 2, 5) (dual of [(16471, 2), 32920, 6]-NRT-code), using
(17, 22, 21512)-Net over F7 — Digital
Digital (17, 22, 21512)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(722, 21512, F7, 5) (dual of [21512, 21490, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(70, 2801, F7, 0) (dual of [2801, 2801, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(70, 2801, F7, 0) (dual of [2801, 2801, 1]-code) (see above)
- linear OA(71, 2801, F7, 1) (dual of [2801, 2800, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(71, 2801, F7, 1) (dual of [2801, 2800, 2]-code) (see above)
- linear OA(71, 2801, F7, 1) (dual of [2801, 2800, 2]-code) (see above)
- linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- Hamming code H(5,7) [i]
- linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- trace code [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- linear OA(70, 2801, F7, 0) (dual of [2801, 2801, 1]-code), using
- generalized (u, u+v)-construction [i] based on
(17, 22, large)-Net in Base 7 — Upper bound on s
There is no (17, 22, large)-net in base 7, because
- 3 times m-reduction [i] would yield (17, 19, large)-net in base 7, but