Best Known (21−12, 21, s)-Nets in Base 32
(21−12, 21, 104)-Net over F32 — Constructive and digital
Digital (9, 21, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
(21−12, 21, 125)-Net over F32 — Digital
Digital (9, 21, 125)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3221, 125, F32, 12) (dual of [125, 104, 13]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 9 times 0, 1, 25 times 0) [i] based on linear OA(3217, 83, F32, 12) (dual of [83, 66, 13]-code), using
- extended algebraic-geometric code AGe(F,70P) [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 83, using
- 38 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 9 times 0, 1, 25 times 0) [i] based on linear OA(3217, 83, F32, 12) (dual of [83, 66, 13]-code), using
(21−12, 21, 258)-Net in Base 32 — Constructive
(9, 21, 258)-net in base 32, using
- base change [i] based on (3, 15, 258)-net in base 128, using
- 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on digital (1, 14, 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, 14, 258)-net over F256, using
- 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
(21−12, 21, 289)-Net in Base 32
(9, 21, 289)-net in base 32, using
- base change [i] based on (3, 15, 289)-net in base 128, using
- 1 times m-reduction [i] based on (3, 16, 289)-net in base 128, using
- base change [i] based on digital (1, 14, 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, 14, 289)-net over F256, using
- 1 times m-reduction [i] based on (3, 16, 289)-net in base 128, using
(21−12, 21, 17898)-Net in Base 32 — Upper bound on s
There is no (9, 21, 17899)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 40 569752 733817 404957 936907 586890 > 3221 [i]