Best Known (77, 77+19, s)-Nets in Base 16
(77, 77+19, 116532)-Net over F16 — Constructive and digital
Digital (77, 96, 116532)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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 (67, 86, 116508)-net over F16, using
- net defined by OOA [i] based on linear OOA(1686, 116508, F16, 19, 19) (dual of [(116508, 19), 2213566, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1686, 1048573, F16, 19) (dual of [1048573, 1048487, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1686, 1048573, F16, 19) (dual of [1048573, 1048487, 20]-code), using
- net defined by OOA [i] based on linear OOA(1686, 116508, F16, 19, 19) (dual of [(116508, 19), 2213566, 20]-NRT-code), using
- digital (1, 10, 24)-net over F16, using
(77, 77+19, 1330500)-Net over F16 — Digital
Digital (77, 96, 1330500)-net over F16, using
(77, 77+19, large)-Net in Base 16 — Upper bound on s
There is no (77, 96, large)-net in base 16, because
- 17 times m-reduction [i] would yield (77, 79, large)-net in base 16, but