Best Known (41, 41+32, s)-Nets in Base 32
(41, 41+32, 240)-Net over F32 — Constructive and digital
Digital (41, 73, 240)-net over F32, using
- 6 times m-reduction [i] based on digital (41, 79, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 30, 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, 49, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 30, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(41, 41+32, 513)-Net in Base 32 — Constructive
(41, 73, 513)-net in base 32, using
- 5 times m-reduction [i] based on (41, 78, 513)-net in base 32, using
- base change [i] based on digital (28, 65, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 65, 513)-net over F64, using
(41, 41+32, 1419)-Net over F32 — Digital
Digital (41, 73, 1419)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3273, 1419, F32, 32) (dual of [1419, 1346, 33]-code), using
- 1345 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 18 times 0, 1, 20 times 0, 1, 23 times 0, 1, 26 times 0, 1, 29 times 0, 1, 33 times 0, 1, 36 times 0, 1, 42 times 0, 1, 46 times 0, 1, 53 times 0, 1, 58 times 0, 1, 66 times 0, 1, 74 times 0, 1, 83 times 0, 1, 93 times 0, 1, 104 times 0, 1, 116 times 0, 1, 131 times 0, 1, 147 times 0) [i] based on linear OA(3232, 33, F32, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,32)), using
- dual of repetition code with length 33 [i]
- 1345 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 18 times 0, 1, 20 times 0, 1, 23 times 0, 1, 26 times 0, 1, 29 times 0, 1, 33 times 0, 1, 36 times 0, 1, 42 times 0, 1, 46 times 0, 1, 53 times 0, 1, 58 times 0, 1, 66 times 0, 1, 74 times 0, 1, 83 times 0, 1, 93 times 0, 1, 104 times 0, 1, 116 times 0, 1, 131 times 0, 1, 147 times 0) [i] based on linear OA(3232, 33, F32, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,32)), using
(41, 41+32, 1615926)-Net in Base 32 — Upper bound on s
There is no (41, 73, 1615927)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 75 153598 076279 545376 637547 999315 079052 515015 189864 202636 447433 430145 119081 443910 073788 978805 839446 664043 703259 > 3273 [i]