Best Known (19, 19+5, s)-Nets in Base 7
(19, 19+5, 16526)-Net over F7 — Constructive and digital
Digital (19, 24, 16526)-net over F7, using
- net defined by OOA [i] based on linear OOA(724, 16526, F7, 6, 5) (dual of [(16526, 6), 99132, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(724, 16527, F7, 2, 5) (dual of [(16527, 2), 33030, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(70, 2361, F7, 2, 0) (dual of [(2361, 2), 4722, 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, 2361, F7, 2, 0) (dual of [(2361, 2), 4722, 1]-NRT-code) (see above)
- linear OOA(71, 2361, F7, 2, 1) (dual of [(2361, 2), 4721, 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, 2361, F7, 2, 1) (dual of [(2361, 2), 4721, 2]-NRT-code) (see above)
- linear OOA(71, 2361, F7, 2, 1) (dual of [(2361, 2), 4721, 2]-NRT-code) (see above)
- linear OOA(75, 2361, F7, 2, 2) (dual of [(2361, 2), 4717, 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(716, 2361, F7, 2, 5) (dual of [(2361, 2), 4706, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(72, 8, F7, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;14,7) [i]
- 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(72, 8, F7, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(70, 2361, F7, 2, 0) (dual of [(2361, 2), 4722, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(724, 16527, F7, 2, 5) (dual of [(16527, 2), 33030, 6]-NRT-code), using
(19, 19+5, 43402)-Net over F7 — Digital
Digital (19, 24, 43402)-net over F7, using
(19, 19+5, large)-Net in Base 7 — Upper bound on s
There is no (19, 24, large)-net in base 7, because
- 3 times m-reduction [i] would yield (19, 21, large)-net in base 7, but