Best Known (24−13, 24, s)-Nets in Base 32
(24−13, 24, 120)-Net over F32 — Constructive and digital
Digital (11, 24, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
(24−13, 24, 218)-Net over F32 — Digital
Digital (11, 24, 218)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3224, 218, F32, 13) (dual of [218, 194, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3224, 341, F32, 13) (dual of [341, 317, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(3224, 341, F32, 13) (dual of [341, 317, 14]-code), using
(24−13, 24, 259)-Net in Base 32 — Constructive
(11, 24, 259)-net in base 32, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
(24−13, 24, 321)-Net in Base 32
(11, 24, 321)-net in base 32, using
- base change [i] based on digital (2, 15, 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
(24−13, 24, 56830)-Net in Base 32 — Upper bound on s
There is no (11, 24, 56831)-net in base 32, because
- 1 times m-reduction [i] would yield (11, 23, 56831)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 41540 617899 068728 667871 245285 343431 > 3223 [i]