Best Known (48, 48+43, s)-Nets in Base 32
(48, 48+43, 240)-Net over F32 — Constructive and digital
Digital (48, 91, 240)-net over F32, using
- 9 times m-reduction [i] based on digital (48, 100, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 37, 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 (11, 63, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 37, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(48, 48+43, 513)-Net in Base 32 — Constructive
(48, 91, 513)-net in base 32, using
- t-expansion [i] based on (46, 91, 513)-net in base 32, using
- 17 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 17 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(48, 48+43, 1029)-Net over F32 — Digital
Digital (48, 91, 1029)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3291, 1029, F32, 43) (dual of [1029, 938, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, 1052, F32, 43) (dual of [1052, 961, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(32) [i] based on
- linear OA(3282, 1024, F32, 43) (dual of [1024, 942, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3263, 1024, F32, 33) (dual of [1024, 961, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(329, 28, F32, 9) (dual of [28, 19, 10]-code or 28-arc in PG(8,32)), using
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- Reed–Solomon code RS(23,32) [i]
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- construction X applied to Ce(42) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(3291, 1052, F32, 43) (dual of [1052, 961, 44]-code), using
(48, 48+43, 790255)-Net in Base 32 — Upper bound on s
There is no (48, 91, 790256)-net in base 32, because
- 1 times m-reduction [i] would yield (48, 90, 790256)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2907 359413 472739 715742 943173 189152 789794 790246 614495 869953 379656 320357 750710 093214 383983 968312 092839 026898 241438 655644 997819 900503 346686 > 3290 [i]