Best Known (23, 23+26, s)-Nets in Base 32
(23, 23+26, 162)-Net over F32 — Constructive and digital
Digital (23, 49, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 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, 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 (3, 16, 64)-net over F32, using
(23, 23+26, 288)-Net in Base 32 — Constructive
(23, 49, 288)-net in base 32, using
- base change [i] based on digital (9, 35, 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
(23, 23+26, 314)-Net over F32 — Digital
Digital (23, 49, 314)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3249, 314, F32, 26) (dual of [314, 265, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3249, 341, F32, 26) (dual of [341, 292, 27]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(3249, 341, F32, 26) (dual of [341, 292, 27]-code), using
(23, 23+26, 321)-Net in Base 32
(23, 49, 321)-net in base 32, using
- 7 times m-reduction [i] based on (23, 56, 321)-net in base 32, using
- base change [i] based on digital (2, 35, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 35, 321)-net over F256, using
(23, 23+26, 86152)-Net in Base 32 — Upper bound on s
There is no (23, 49, 86153)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 56 540236 625416 081934 264055 873481 381603 075550 846078 902797 242794 494267 487872 > 3249 [i]