Best Known (93−44, 93, s)-Nets in Base 32
(93−44, 93, 240)-Net over F32 — Constructive and digital
Digital (49, 93, 240)-net over F32, using
- 10 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
(93−44, 93, 513)-Net in Base 32 — Constructive
(49, 93, 513)-net in base 32, using
- t-expansion [i] based on (46, 93, 513)-net in base 32, using
- 15 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
- 15 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(93−44, 93, 1036)-Net over F32 — Digital
Digital (49, 93, 1036)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3293, 1036, F32, 44) (dual of [1036, 943, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 1053, F32, 44) (dual of [1053, 960, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(33) [i] based on
- linear OA(3284, 1024, F32, 44) (dual of [1024, 940, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3264, 1024, F32, 34) (dual of [1024, 960, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(329, 29, F32, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,32)), using
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- Reed–Solomon code RS(23,32) [i]
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- construction X applied to Ce(43) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(3293, 1053, F32, 44) (dual of [1053, 960, 45]-code), using
(93−44, 93, 673230)-Net in Base 32 — Upper bound on s
There is no (49, 93, 673231)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 95 270858 686152 089132 743745 698342 184061 654154 300221 452953 319298 589914 713817 366608 693101 278318 759820 600074 622310 484628 881796 894519 923978 189012 > 3293 [i]