Best Known (96−47, 96, s)-Nets in Base 32
(96−47, 96, 240)-Net over F32 — Constructive and digital
Digital (49, 96, 240)-net over F32, using
- 7 times m-reduction [i] based on digital (49, 103, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 38, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 65, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 38, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(96−47, 96, 513)-Net in Base 32 — Constructive
(49, 96, 513)-net in base 32, using
- t-expansion [i] based on (46, 96, 513)-net in base 32, using
- 12 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 12 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(96−47, 96, 835)-Net over F32 — Digital
Digital (49, 96, 835)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3296, 835, F32, 47) (dual of [835, 739, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, 1036, F32, 47) (dual of [1036, 940, 48]-code), using
- construction X applied to C([0,23]) ⊂ C([0,21]) [i] based on
- linear OA(3293, 1025, F32, 47) (dual of [1025, 932, 48]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,23], and minimum distance d ≥ |{−23,−22,…,23}|+1 = 48 (BCH-bound) [i]
- linear OA(3285, 1025, F32, 43) (dual of [1025, 940, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to C([0,23]) ⊂ C([0,21]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3296, 1036, F32, 47) (dual of [1036, 940, 48]-code), using
(96−47, 96, 501196)-Net in Base 32 — Upper bound on s
There is no (49, 96, 501197)-net in base 32, because
- 1 times m-reduction [i] would yield (49, 95, 501197)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 97555 820221 894056 886930 066955 076629 724870 477373 207223 925166 222453 040696 317985 204016 081857 134176 388271 957536 911562 909696 876648 206816 721389 175200 > 3295 [i]