Best Known (92, 92+27, s)-Nets in Base 16
(92, 92+27, 10099)-Net over F16 — Constructive and digital
Digital (92, 119, 10099)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (79, 106, 10082)-net over F16, using
- net defined by OOA [i] based on linear OOA(16106, 10082, F16, 27, 27) (dual of [(10082, 27), 272108, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16106, 131067, F16, 27) (dual of [131067, 130961, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16106, 131074, F16, 27) (dual of [131074, 130968, 28]-code), using
- trace code [i] based on linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- trace code [i] based on linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16106, 131074, F16, 27) (dual of [131074, 130968, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16106, 131067, F16, 27) (dual of [131067, 130961, 28]-code), using
- net defined by OOA [i] based on linear OOA(16106, 10082, F16, 27, 27) (dual of [(10082, 27), 272108, 28]-NRT-code), using
- digital (0, 13, 17)-net over F16, using
(92, 92+27, 20165)-Net in Base 16 — Constructive
(92, 119, 20165)-net in base 16, using
- net defined by OOA [i] based on OOA(16119, 20165, S16, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(16119, 262146, S16, 27), using
- discarding factors based on OA(16119, 262147, S16, 27), using
- discarding parts of the base [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- discarding factors based on OA(16119, 262147, S16, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(16119, 262146, S16, 27), using
(92, 92+27, 228240)-Net over F16 — Digital
Digital (92, 119, 228240)-net over F16, using
(92, 92+27, large)-Net in Base 16 — Upper bound on s
There is no (92, 119, large)-net in base 16, because
- 25 times m-reduction [i] would yield (92, 94, large)-net in base 16, but