Best Known (22−12, 22, s)-Nets in Base 32
(22−12, 22, 108)-Net over F32 — Constructive and digital
Digital (10, 22, 108)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (3, 15, 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 (1, 7, 44)-net over F32, using
(22−12, 22, 208)-Net over F32 — Digital
Digital (10, 22, 208)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3222, 208, F32, 12) (dual of [208, 186, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 341, F32, 12) (dual of [341, 319, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3222, 341, F32, 12) (dual of [341, 319, 13]-code), using
(22−12, 22, 258)-Net in Base 32 — Constructive
(10, 22, 258)-net in base 32, using
- 2 times m-reduction [i] based on (10, 24, 258)-net in base 32, using
- base change [i] based on digital (1, 15, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 15, 258)-net over F256, using
(22−12, 22, 289)-Net in Base 32
(10, 22, 289)-net in base 32, using
- 2 times m-reduction [i] based on (10, 24, 289)-net in base 32, using
- base change [i] based on digital (1, 15, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 15, 289)-net over F256, using
(22−12, 22, 31893)-Net in Base 32 — Upper bound on s
There is no (10, 22, 31894)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1298 110482 089498 352779 619987 257080 > 3222 [i]