Best Known (51−27, 51, s)-Nets in Base 32
(51−27, 51, 162)-Net over F32 — Constructive and digital
Digital (24, 51, 162)-net over F32, using
- 1 times m-reduction [i] based on digital (24, 52, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (7, 35, 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 (3, 17, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(51−27, 51, 260)-Net in Base 32 — Constructive
(24, 51, 260)-net in base 32, using
- 5 times m-reduction [i] based on (24, 56, 260)-net in base 32, using
- base change [i] based on digital (3, 35, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 35, 260)-net over F256, using
(51−27, 51, 326)-Net over F32 — Digital
Digital (24, 51, 326)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3251, 326, F32, 27) (dual of [326, 275, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3251, 341, F32, 27) (dual of [341, 290, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3251, 341, F32, 27) (dual of [341, 290, 28]-code), using
(51−27, 51, 112475)-Net in Base 32 — Upper bound on s
There is no (24, 51, 112476)-net in base 32, because
- 1 times m-reduction [i] would yield (24, 50, 112476)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1809 348125 848975 972882 957799 598594 878247 998250 615085 386997 870134 101938 109492 > 3250 [i]