Best Known (68, 68+17, s)-Nets in Base 16
(68, 68+17, 131095)-Net over F16 — Constructive and digital
Digital (68, 85, 131095)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- 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
- net defined by OOA [i] based on linear OOA(1676, 131071, F16, 17, 17) (dual of [(131071, 17), 2228131, 18]-NRT-code), using
- digital (1, 9, 24)-net over F16, using
(68, 68+17, 1130675)-Net over F16 — Digital
Digital (68, 85, 1130675)-net over F16, using
(68, 68+17, large)-Net in Base 16 — Upper bound on s
There is no (68, 85, large)-net in base 16, because
- 15 times m-reduction [i] would yield (68, 70, large)-net in base 16, but