Best Known (73, 73+24, s)-Nets in Base 16
(73, 73+24, 10923)-Net over F16 — Constructive and digital
Digital (73, 97, 10923)-net over F16, using
- 163 times duplication [i] based on digital (70, 94, 10923)-net over F16, using
- net defined by OOA [i] based on linear OOA(1694, 10923, F16, 24, 24) (dual of [(10923, 24), 262058, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(1694, 131076, F16, 24) (dual of [131076, 130982, 25]-code), using
- trace code [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- trace code [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(1694, 131076, F16, 24) (dual of [131076, 130982, 25]-code), using
- net defined by OOA [i] based on linear OOA(1694, 10923, F16, 24, 24) (dual of [(10923, 24), 262058, 25]-NRT-code), using
(73, 73+24, 108407)-Net over F16 — Digital
Digital (73, 97, 108407)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1697, 108407, F16, 24) (dual of [108407, 108310, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(1697, 131083, F16, 24) (dual of [131083, 130986, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1696, 131082, F16, 24) (dual of [131082, 130986, 25]-code), using
- trace code [i] based on linear OA(25648, 65541, F256, 24) (dual of [65541, 65493, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- trace code [i] based on linear OA(25648, 65541, F256, 24) (dual of [65541, 65493, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1696, 131082, F16, 24) (dual of [131082, 130986, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(1697, 131083, F16, 24) (dual of [131083, 130986, 25]-code), using
(73, 73+24, large)-Net in Base 16 — Upper bound on s
There is no (73, 97, large)-net in base 16, because
- 22 times m-reduction [i] would yield (73, 75, large)-net in base 16, but