Best Known (37, 65, s)-Nets in Base 32
(37, 65, 240)-Net over F32 — Constructive and digital
Digital (37, 65, 240)-net over F32, using
- 2 times m-reduction [i] based on digital (37, 67, 240)-net over F32, using
- (u, u+v)-construction [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
- digital (11, 41, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 26, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(37, 65, 354)-Net in Base 32 — Constructive
(37, 65, 354)-net in base 32, using
- (u, u+v)-construction [i] based on
- (9, 23, 257)-net in base 32, using
- 1 times m-reduction [i] based on (9, 24, 257)-net in base 32, using
- base change [i] based on digital (0, 15, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 15, 257)-net over F256, using
- 1 times m-reduction [i] based on (9, 24, 257)-net in base 32, using
- (14, 42, 177)-net in base 32, using
- base change [i] based on digital (7, 35, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 35, 177)-net over F64, using
- (9, 23, 257)-net in base 32, using
(37, 65, 1495)-Net over F32 — Digital
Digital (37, 65, 1495)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3265, 1495, F32, 28) (dual of [1495, 1430, 29]-code), using
- 1425 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 21 times 0, 1, 24 times 0, 1, 27 times 0, 1, 32 times 0, 1, 36 times 0, 1, 41 times 0, 1, 48 times 0, 1, 54 times 0, 1, 62 times 0, 1, 71 times 0, 1, 80 times 0, 1, 92 times 0, 1, 105 times 0, 1, 119 times 0, 1, 136 times 0, 1, 155 times 0, 1, 177 times 0) [i] based on linear OA(3228, 33, F32, 28) (dual of [33, 5, 29]-code or 33-arc in PG(27,32)), using
- extended Reed–Solomon code RSe(5,32) [i]
- 1425 step Varšamov–Edel lengthening with (ri) = (5, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 21 times 0, 1, 24 times 0, 1, 27 times 0, 1, 32 times 0, 1, 36 times 0, 1, 41 times 0, 1, 48 times 0, 1, 54 times 0, 1, 62 times 0, 1, 71 times 0, 1, 80 times 0, 1, 92 times 0, 1, 105 times 0, 1, 119 times 0, 1, 136 times 0, 1, 155 times 0, 1, 177 times 0) [i] based on linear OA(3228, 33, F32, 28) (dual of [33, 5, 29]-code or 33-arc in PG(27,32)), using
(37, 65, 1897976)-Net in Base 32 — Upper bound on s
There is no (37, 65, 1897977)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 68 351943 023990 656335 031329 260219 336241 249786 711175 876379 299489 999222 547148 226100 263295 357765 161272 > 3265 [i]