Best Known (59, 76, s)-Nets in Base 16
(59, 76, 131071)-Net over F16 — Constructive and digital
Digital (59, 76, 131071)-net over F16, using
- net defined by OOA [i] based on linear OOA(1676, 131071, F16, 17, 17) (dual of [(131071, 17), 2228131, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1676, 1048569, F16, 17) (dual of [1048569, 1048493, 18]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1676, 1048569, F16, 17) (dual of [1048569, 1048493, 18]-code), using
(59, 76, 524288)-Net over F16 — Digital
Digital (59, 76, 524288)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1676, 524288, F16, 2, 17) (dual of [(524288, 2), 1048500, 18]-NRT-code), using
- OOA 2-folding [i] based on 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]
- OOA 2-folding [i] based on linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using
(59, 76, large)-Net in Base 16 — Upper bound on s
There is no (59, 76, large)-net in base 16, because
- 15 times m-reduction [i] would yield (59, 61, large)-net in base 16, but