Best Known (38, 72, s)-Nets in Base 32
(38, 72, 224)-Net over F32 — Constructive and digital
Digital (38, 72, 224)-net over F32, using
- 2 times m-reduction [i] based on digital (38, 74, 224)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 27, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (11, 47, 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 (9, 27, 104)-net over F32, using
- (u, u+v)-construction [i] based on
(38, 72, 290)-Net in Base 32 — Constructive
(38, 72, 290)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 17, 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
- (21, 55, 257)-net in base 32, using
- 1 times m-reduction [i] based on (21, 56, 257)-net in base 32, using
- base change [i] based on digital (0, 35, 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
- base change [i] based on digital (0, 35, 257)-net over F256, using
- 1 times m-reduction [i] based on (21, 56, 257)-net in base 32, using
- digital (0, 17, 33)-net over F32, using
(38, 72, 887)-Net over F32 — Digital
Digital (38, 72, 887)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3272, 887, F32, 34) (dual of [887, 815, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3272, 1047, F32, 34) (dual of [1047, 975, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- 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(3249, 1024, F32, 25) (dual of [1024, 975, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(328, 23, F32, 8) (dual of [23, 15, 9]-code or 23-arc in PG(7,32)), using
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- Reed–Solomon code RS(24,32) [i]
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3272, 1047, F32, 34) (dual of [1047, 975, 35]-code), using
(38, 72, 548693)-Net in Base 32 — Upper bound on s
There is no (38, 72, 548694)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 348599 113257 030210 842340 985711 313689 319108 414953 994669 275096 339553 448365 740126 654919 346109 944827 536096 349987 > 3272 [i]