Best Known (49, 95, s)-Nets in Base 32
(49, 95, 240)-Net over F32 — Constructive and digital
Digital (49, 95, 240)-net over F32, using
- 8 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
(49, 95, 513)-Net in Base 32 — Constructive
(49, 95, 513)-net in base 32, using
- t-expansion [i] based on (46, 95, 513)-net in base 32, using
- 13 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
- 13 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(49, 95, 894)-Net over F32 — Digital
Digital (49, 95, 894)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3295, 894, F32, 46) (dual of [894, 799, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3295, 1047, F32, 46) (dual of [1047, 952, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(37) [i] based on
- linear OA(3288, 1024, F32, 46) (dual of [1024, 936, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3272, 1024, F32, 38) (dual of [1024, 952, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(327, 23, F32, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(45) ⊂ Ce(37) [i] based on
- discarding factors / shortening the dual code based on linear OA(3295, 1047, F32, 46) (dual of [1047, 952, 47]-code), using
(49, 95, 501196)-Net in Base 32 — Upper bound on s
There is no (49, 95, 501197)-net in base 32, because
- 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]