Best Known (73, 73+20, s)-Nets in Base 16
(73, 73+20, 104859)-Net over F16 — Constructive and digital
Digital (73, 93, 104859)-net over F16, using
- net defined by OOA [i] based on linear OOA(1693, 104859, F16, 20, 20) (dual of [(104859, 20), 2097087, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(1693, 1048590, F16, 20) (dual of [1048590, 1048497, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(1693, 1048590, F16, 20) (dual of [1048590, 1048497, 21]-code), using
(73, 73+20, 718496)-Net over F16 — Digital
Digital (73, 93, 718496)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1693, 718496, F16, 20) (dual of [718496, 718403, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code), using
(73, 73+20, large)-Net in Base 16 — Upper bound on s
There is no (73, 93, large)-net in base 16, because
- 18 times m-reduction [i] would yield (73, 75, large)-net in base 16, but