Best Known (26−14, 26, s)-Nets in Base 32
(26−14, 26, 120)-Net over F32 — Constructive and digital
Digital (12, 26, 120)-net over F32, using
- t-expansion [i] based on digital (11, 26, 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
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(26−14, 26, 228)-Net over F32 — Digital
Digital (12, 26, 228)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3226, 228, F32, 14) (dual of [228, 202, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3226, 341, F32, 14) (dual of [341, 315, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3226, 341, F32, 14) (dual of [341, 315, 15]-code), using
(26−14, 26, 258)-Net in Base 32 — Constructive
(12, 26, 258)-net in base 32, using
- 2 times m-reduction [i] based on (12, 28, 258)-net in base 32, using
- base change [i] based on (4, 20, 258)-net in base 128, using
- 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- base change [i] based on digital (1, 21, 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, 21, 258)-net over F256, using
- 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- base change [i] based on (4, 20, 258)-net in base 128, using
(26−14, 26, 289)-Net in Base 32
(12, 26, 289)-net in base 32, using
- 2 times m-reduction [i] based on (12, 28, 289)-net in base 32, using
- base change [i] based on (4, 20, 289)-net in base 128, using
- 4 times m-reduction [i] based on (4, 24, 289)-net in base 128, using
- base change [i] based on digital (1, 21, 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, 21, 289)-net over F256, using
- 4 times m-reduction [i] based on (4, 24, 289)-net in base 128, using
- base change [i] based on (4, 20, 289)-net in base 128, using
(26−14, 26, 42469)-Net in Base 32 — Upper bound on s
There is no (12, 26, 42470)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1361 156438 225960 602262 503240 999495 028400 > 3226 [i]