Best Known (22−5, 22, s)-Nets in Base 16
(22−5, 22, 1044495)-Net over F16 — Constructive and digital
Digital (17, 22, 1044495)-net over F16, using
- net defined by OOA [i] based on linear OOA(1622, 1044495, F16, 6, 5) (dual of [(1044495, 6), 6266948, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(1622, 1044496, F16, 2, 5) (dual of [(1044496, 2), 2088970, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(160, s, F16, 2, 0) with arbitrarily large s, using
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
- linear OOA(161, 65281, F16, 2, 1) (dual of [(65281, 2), 130561, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(161, s, F16, 2, 1) with arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(161, s, F16, 2, 1) with arbitrarily large s, using
- linear OOA(161, 65281, F16, 2, 1) (dual of [(65281, 2), 130561, 2]-NRT-code) (see above)
- linear OOA(161, 65281, F16, 2, 1) (dual of [(65281, 2), 130561, 2]-NRT-code) (see above)
- linear OOA(165, 65281, F16, 2, 2) (dual of [(65281, 2), 130557, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(165, 69905, F16, 2, 2) (dual of [(69905, 2), 139805, 3]-NRT-code), using
- appending kth column [i] based on linear OA(165, 69905, F16, 2) (dual of [69905, 69900, 3]-code), using
- Hamming code H(5,16) [i]
- appending kth column [i] based on linear OA(165, 69905, F16, 2) (dual of [69905, 69900, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(165, 69905, F16, 2, 2) (dual of [(69905, 2), 139805, 3]-NRT-code), using
- linear OOA(1614, 65281, F16, 2, 5) (dual of [(65281, 2), 130548, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OOA 2-folding [i] based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- linear OOA(160, 65281, F16, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(1622, 1044496, F16, 2, 5) (dual of [(1044496, 2), 2088970, 6]-NRT-code), using
(22−5, 22, 1179137)-Net over F16 — Digital
Digital (17, 22, 1179137)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1622, 1179137, F16, 5) (dual of [1179137, 1179115, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code) (see above)
- linear OA(161, 69905, F16, 1) (dual of [69905, 69904, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(161, 69905, F16, 1) (dual of [69905, 69904, 2]-code) (see above)
- linear OA(161, 69905, F16, 1) (dual of [69905, 69904, 2]-code) (see above)
- linear OA(165, 69905, F16, 2) (dual of [69905, 69900, 3]-code), using
- Hamming code H(5,16) [i]
- linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- linear OA(160, 69905, F16, 0) (dual of [69905, 69905, 1]-code), using
- generalized (u, u+v)-construction [i] based on
(22−5, 22, large)-Net in Base 16 — Upper bound on s
There is no (17, 22, large)-net in base 16, because
- 3 times m-reduction [i] would yield (17, 19, large)-net in base 16, but