Best Known (50, 99, s)-Nets in Base 32
(50, 99, 240)-Net over F32 — Constructive and digital
Digital (50, 99, 240)-net over F32, using
- 7 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, 99, 513)-Net in Base 32 — Constructive
(50, 99, 513)-net in base 32, using
- t-expansion [i] based on (46, 99, 513)-net in base 32, using
- 9 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
- 9 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(50, 99, 794)-Net over F32 — Digital
Digital (50, 99, 794)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3299, 794, F32, 49) (dual of [794, 695, 50]-code), using
- discarding factors / shortening the dual code based on linear OA(3299, 1041, F32, 49) (dual of [1041, 942, 50]-code), using
- construction X applied to Ce(48) ⊂ Ce(42) [i] based on
- linear OA(3294, 1024, F32, 49) (dual of [1024, 930, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- 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(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(48) ⊂ Ce(42) [i] based on
- discarding factors / shortening the dual code based on linear OA(3299, 1041, F32, 49) (dual of [1041, 942, 50]-code), using
(50, 99, 442606)-Net in Base 32 — Upper bound on s
There is no (50, 99, 442607)-net in base 32, because
- 1 times m-reduction [i] would yield (50, 98, 442607)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3196 706032 384510 600524 317121 311923 561937 458140 950022 698065 472801 190234 827977 177028 250983 166371 221964 374736 897679 870561 139406 733057 162176 568377 002034 > 3298 [i]