Best Known (50, 50+46, s)-Nets in Base 32
(50, 50+46, 240)-Net over F32 — Constructive and digital
Digital (50, 96, 240)-net over F32, using
- 10 times m-reduction [i] based on digital (50, 106, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 39, 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, 67, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 39, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(50, 50+46, 513)-Net in Base 32 — Constructive
(50, 96, 513)-net in base 32, using
- t-expansion [i] based on (46, 96, 513)-net in base 32, using
- 12 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
- 12 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(50, 50+46, 969)-Net over F32 — Digital
Digital (50, 96, 969)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3296, 969, F32, 46) (dual of [969, 873, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, 1050, F32, 46) (dual of [1050, 954, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(36) [i] based on
- linear OA(3288, 1024, F32, 46) (dual of [1024, 936, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3270, 1024, F32, 37) (dual of [1024, 954, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(328, 26, F32, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,32)), using
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- Reed–Solomon code RS(24,32) [i]
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- construction X applied to Ce(45) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(3296, 1050, F32, 46) (dual of [1050, 954, 47]-code), using
(50, 50+46, 582707)-Net in Base 32 — Upper bound on s
There is no (50, 96, 582708)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3 121751 721152 771101 016801 888303 450110 420037 726664 243293 959760 256862 397791 834340 175620 726983 153854 030406 788352 145486 401427 071266 345925 171057 843784 > 3296 [i]