Best Known (22, 46, s)-Nets in Base 32
(22, 46, 162)-Net over F32 — Constructive and digital
Digital (22, 46, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- 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 (7, 31, 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, 15, 64)-net over F32, using
(22, 46, 261)-Net in Base 32 — Constructive
(22, 46, 261)-net in base 32, using
- 2 times m-reduction [i] based on (22, 48, 261)-net in base 32, using
- base change [i] based on digital (4, 30, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- base change [i] based on digital (4, 30, 261)-net over F256, using
(22, 46, 341)-Net over F32 — Digital
Digital (22, 46, 341)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3246, 341, F32, 24) (dual of [341, 295, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 346, F32, 24) (dual of [346, 300, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(3245, 342, F32, 24) (dual of [342, 297, 25]-code), using an extension Ce(23) of the narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3242, 342, F32, 22) (dual of [342, 300, 23]-code), using an extension Ce(21) of the narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(321, 4, F32, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 346, F32, 24) (dual of [346, 300, 25]-code), using
(22, 46, 100395)-Net in Base 32 — Upper bound on s
There is no (22, 46, 100396)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1725 463851 979469 258403 486455 526142 310988 707788 657464 053266 306549 630584 > 3246 [i]