Best Known (118−16, 118, s)-Nets in Base 16
(118−16, 118, 2098195)-Net over F16 — Constructive and digital
Digital (102, 118, 2098195)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (18, 26, 1045)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 17)-net over F16, using
- digital (4, 8, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 4, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 4, 257)-net over F256, using
- digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (76, 92, 2097150)-net over F16, using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- digital (18, 26, 1045)-net over F16, using
(118−16, 118, 2098206)-Net in Base 16 — Constructive
(102, 118, 2098206)-net in base 16, using
- 161 times duplication [i] based on (101, 117, 2098206)-net in base 16, using
- (u, u+v)-construction [i] based on
- (17, 25, 1056)-net in base 16, using
- base change [i] based on digital (12, 20, 1056)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 33)-net over F32, using
- s-reduction based on digital (0, 0, s)-net over F32 with arbitrarily large s, using
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 0, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 0, 33)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- base change [i] based on digital (12, 20, 1056)-net over F32, using
- digital (76, 92, 2097150)-net over F16, using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- (17, 25, 1056)-net in base 16, using
- (u, u+v)-construction [i] based on
(118−16, 118, large)-Net over F16 — Digital
Digital (102, 118, large)-net over F16, using
- t-expansion [i] based on digital (99, 118, large)-net over F16, using
- 3 times m-reduction [i] based on digital (99, 121, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- 3 times m-reduction [i] based on digital (99, 121, large)-net over F16, using
(118−16, 118, large)-Net in Base 16 — Upper bound on s
There is no (102, 118, large)-net in base 16, because
- 14 times m-reduction [i] would yield (102, 104, large)-net in base 16, but