Best Known (41, 83, s)-Nets in Base 32
(41, 83, 224)-Net over F32 — Constructive and digital
Digital (41, 83, 224)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 30, 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, 53, 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, 30, 104)-net over F32, using
(41, 83, 288)-Net in Base 32 — Constructive
(41, 83, 288)-net in base 32, using
- t-expansion [i] based on (40, 83, 288)-net in base 32, using
- 25 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 25 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(41, 83, 602)-Net over F32 — Digital
Digital (41, 83, 602)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3283, 602, F32, 42) (dual of [602, 519, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3283, 1035, F32, 42) (dual of [1035, 952, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(37) [i] based on
- linear OA(3280, 1024, F32, 42) (dual of [1024, 944, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [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(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(41) ⊂ Ce(37) [i] based on
- discarding factors / shortening the dual code based on linear OA(3283, 1035, F32, 42) (dual of [1035, 952, 43]-code), using
(41, 83, 248907)-Net in Base 32 — Upper bound on s
There is no (41, 83, 248908)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 84617 236087 124230 926841 220265 665721 295688 966080 638472 354307 916867 622392 997959 921720 855863 947788 376900 428907 177709 355435 347832 > 3283 [i]