Best Known (49−24, 49, s)-Nets in Base 32
(49−24, 49, 174)-Net over F32 — Constructive and digital
Digital (25, 49, 174)-net over F32, using
- 2 times m-reduction [i] based on digital (25, 51, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 33, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (5, 18, 76)-net over F32, using
- (u, u+v)-construction [i] based on
(49−24, 49, 288)-Net in Base 32 — Constructive
(25, 49, 288)-net in base 32, using
- 7 times m-reduction [i] based on (25, 56, 288)-net in base 32, using
- base change [i] based on digital (9, 40, 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, 40, 288)-net over F128, using
(49−24, 49, 552)-Net over F32 — Digital
Digital (25, 49, 552)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3249, 552, F32, 24) (dual of [552, 503, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3249, 1032, F32, 24) (dual of [1032, 983, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(3247, 1024, F32, 24) (dual of [1024, 977, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3241, 1024, F32, 21) (dual of [1024, 983, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3249, 1032, F32, 24) (dual of [1032, 983, 25]-code), using
(49−24, 49, 238791)-Net in Base 32 — Upper bound on s
There is no (25, 49, 238792)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 56 541733 435692 859781 145113 951073 086822 385027 532869 223605 297809 936206 496232 > 3249 [i]