Best Known (35−20, 35, s)-Nets in Base 32
(35−20, 35, 120)-Net over F32 — Constructive and digital
Digital (15, 35, 120)-net over F32, using
- t-expansion [i] based on digital (11, 35, 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
(35−20, 35, 162)-Net over F32 — Digital
Digital (15, 35, 162)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3235, 162, F32, 20) (dual of [162, 127, 21]-code), using
- 15 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0) [i] based on linear OA(3234, 146, F32, 20) (dual of [146, 112, 21]-code), using
- extended algebraic-geometric code AGe(F,125P) [i] based on function field F/F32 with g(F) = 14 and N(F) ≥ 146, using
- 15 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0) [i] based on linear OA(3234, 146, F32, 20) (dual of [146, 112, 21]-code), using
(35−20, 35, 258)-Net in Base 32 — Constructive
(15, 35, 258)-net in base 32, using
- 1 times m-reduction [i] based on (15, 36, 258)-net in base 32, using
- base change [i] based on (9, 30, 258)-net in base 64, using
- 2 times m-reduction [i] based on (9, 32, 258)-net in base 64, using
- base change [i] based on digital (1, 24, 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, 24, 258)-net over F256, using
- 2 times m-reduction [i] based on (9, 32, 258)-net in base 64, using
- base change [i] based on (9, 30, 258)-net in base 64, using
(35−20, 35, 289)-Net in Base 32
(15, 35, 289)-net in base 32, using
- 1 times m-reduction [i] based on (15, 36, 289)-net in base 32, using
- base change [i] based on (9, 30, 289)-net in base 64, using
- 2 times m-reduction [i] based on (9, 32, 289)-net in base 64, using
- base change [i] based on digital (1, 24, 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, 24, 289)-net over F256, using
- 2 times m-reduction [i] based on (9, 32, 289)-net in base 64, using
- base change [i] based on (9, 30, 289)-net in base 64, using
(35−20, 35, 27074)-Net in Base 32 — Upper bound on s
There is no (15, 35, 27075)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 47897 408741 352997 176137 694347 404378 658345 560200 860776 > 3235 [i]