Best Known (44−20, 44, s)-Nets in Base 32
(44−20, 44, 196)-Net over F32 — Constructive and digital
Digital (24, 44, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 17, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 27, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 17, 98)-net over F32, using
(44−20, 44, 322)-Net in Base 32 — Constructive
(24, 44, 322)-net in base 32, using
- (u, u+v)-construction [i] based on
- (2, 12, 65)-net in base 32, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base change [i] based on digital (0, 10, 65)-net over F64, using
- (12, 32, 257)-net in base 32, using
- base change [i] based on digital (0, 20, 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, 20, 257)-net over F256, using
- (2, 12, 65)-net in base 32, using
(44−20, 44, 952)-Net over F32 — Digital
Digital (24, 44, 952)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3244, 952, F32, 20) (dual of [952, 908, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3244, 1041, F32, 20) (dual of [1041, 997, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(3239, 1024, F32, 20) (dual of [1024, 985, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3227, 1024, F32, 14) (dual of [1024, 997, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3244, 1041, F32, 20) (dual of [1041, 997, 21]-code), using
(44−20, 44, 612732)-Net in Base 32 — Upper bound on s
There is no (24, 44, 612733)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1 685003 451304 167253 160373 939623 627887 506100 823511 110251 623466 028798 > 3244 [i]