Best Known (38, 38+36, s)-Nets in Base 32
(38, 38+36, 224)-Net over F32 — Constructive and digital
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
(38, 38+36, 288)-Net in Base 32 — Constructive
(38, 74, 288)-net in base 32, using
- t-expansion [i] based on (37, 74, 288)-net in base 32, using
- 24 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 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, 70, 288)-net over F128, using
- 24 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
(38, 38+36, 729)-Net over F32 — Digital
Digital (38, 74, 729)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3274, 729, F32, 36) (dual of [729, 655, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3274, 1041, F32, 36) (dual of [1041, 967, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- linear OA(3268, 1024, F32, 36) (dual of [1024, 956, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3257, 1024, F32, 29) (dual of [1024, 967, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(326, 17, F32, 6) (dual of [17, 11, 7]-code or 17-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3274, 1041, F32, 36) (dual of [1041, 967, 37]-code), using
(38, 38+36, 375488)-Net in Base 32 — Upper bound on s
There is no (38, 74, 375489)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2404 963302 856162 943019 216522 342862 093788 817680 567675 233450 207955 290363 105163 980281 860097 797467 894223 041331 637024 > 3274 [i]