Best Known (40, 80, s)-Nets in Base 32
(40, 80, 224)-Net over F32 — Constructive and digital
Digital (40, 80, 224)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 29, 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, 51, 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, 29, 104)-net over F32, using
(40, 80, 288)-Net in Base 32 — Constructive
(40, 80, 288)-net in base 32, using
- 28 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
(40, 80, 635)-Net over F32 — Digital
Digital (40, 80, 635)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3280, 635, F32, 40) (dual of [635, 555, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3280, 1038, F32, 40) (dual of [1038, 958, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(34) [i] based on
- linear OA(3276, 1024, F32, 40) (dual of [1024, 948, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- 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(324, 14, F32, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(39) ⊂ Ce(34) [i] based on
- discarding factors / shortening the dual code based on linear OA(3280, 1038, F32, 40) (dual of [1038, 958, 41]-code), using
(40, 80, 280885)-Net in Base 32 — Upper bound on s
There is no (40, 80, 280886)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 582407 905507 844687 335433 102133 420981 112237 503661 377368 566268 930613 387999 249836 019878 761803 976792 101083 801503 453661 921139 > 3280 [i]