Best Known (38, 38+35, s)-Nets in Base 32
(38, 38+35, 224)-Net over F32 — Constructive and digital
Digital (38, 73, 224)-net over F32, using
- 1 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, 38+35, 290)-Net in Base 32 — Constructive
(38, 73, 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, 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
- digital (0, 17, 33)-net over F32, using
(38, 38+35, 801)-Net over F32 — Digital
Digital (38, 73, 801)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3273, 801, F32, 35) (dual of [801, 728, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3273, 1044, F32, 35) (dual of [1044, 971, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(26) [i] based on
- linear OA(3266, 1024, F32, 35) (dual of [1024, 958, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3253, 1024, F32, 27) (dual of [1024, 971, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(327, 20, F32, 7) (dual of [20, 13, 8]-code or 20-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(34) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(3273, 1044, F32, 35) (dual of [1044, 971, 36]-code), using
(38, 38+35, 548693)-Net in Base 32 — Upper bound on s
There is no (38, 73, 548694)-net in base 32, because
- 1 times m-reduction [i] would yield (38, 72, 548694)-net in base 32, but
- 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]