Best Known (24−5, 24, s)-Nets in Base 16
(24−5, 24, 1044767)-Net over F16 — Constructive and digital
Digital (19, 24, 1044767)-net over F16, using
- net defined by OOA [i] based on linear OOA(1624, 1044767, F16, 6, 5) (dual of [(1044767, 6), 6268578, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(1624, 1044768, F16, 2, 5) (dual of [(1044768, 2), 2089512, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 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, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code) (see above)
- linear OOA(161, 65298, F16, 2, 1) (dual of [(65298, 2), 130595, 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, 65298, F16, 2, 1) (dual of [(65298, 2), 130595, 2]-NRT-code) (see above)
- linear OOA(161, 65298, F16, 2, 1) (dual of [(65298, 2), 130595, 2]-NRT-code) (see above)
- linear OOA(165, 65298, F16, 2, 2) (dual of [(65298, 2), 130591, 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(1616, 65298, F16, 2, 5) (dual of [(65298, 2), 130580, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(162, 17, F16, 2, 2) (dual of [(17, 2), 32, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;32,16) [i]
- 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(162, 17, F16, 2, 2) (dual of [(17, 2), 32, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(160, 65298, F16, 2, 0) (dual of [(65298, 2), 130596, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(1624, 1044768, F16, 2, 5) (dual of [(1044768, 2), 2089512, 6]-NRT-code), using
(24−5, 24, 1048577)-Net in Base 16 — Constructive
(19, 24, 1048577)-net in base 16, using
- 161 times duplication [i] based on (18, 23, 1048577)-net in base 16, using
- net defined by OOA [i] based on OOA(1623, 1048577, S16, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(1623, 2097155, S16, 5), using
- discarding parts of the base [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding parts of the base [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(1623, 2097155, S16, 5), using
- net defined by OOA [i] based on OOA(1623, 1048577, S16, 5, 5), using
(24−5, 24, 2475607)-Net over F16 — Digital
Digital (19, 24, 2475607)-net over F16, using
(24−5, 24, large)-Net in Base 16 — Upper bound on s
There is no (19, 24, large)-net in base 16, because
- 3 times m-reduction [i] would yield (19, 21, large)-net in base 16, but