Best Known (39−22, 39, s)-Nets in Base 32
(39−22, 39, 128)-Net over F32 — Constructive and digital
Digital (17, 39, 128)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (3, 25, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (3, 14, 64)-net over F32, using
(39−22, 39, 186)-Net over F32 — Digital
Digital (17, 39, 186)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3239, 186, F32, 22) (dual of [186, 147, 23]-code), using
- 26 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 21 times 0) [i] based on linear OA(3237, 158, F32, 22) (dual of [158, 121, 23]-code), using
- extended algebraic-geometric code AGe(F,135P) [i] based on function field F/F32 with g(F) = 15 and N(F) ≥ 158, using
- 26 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 21 times 0) [i] based on linear OA(3237, 158, F32, 22) (dual of [158, 121, 23]-code), using
(39−22, 39, 259)-Net in Base 32 — Constructive
(17, 39, 259)-net in base 32, using
- 1 times m-reduction [i] based on (17, 40, 259)-net in base 32, using
- base change [i] based on digital (2, 25, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 25, 259)-net over F256, using
(39−22, 39, 321)-Net in Base 32
(17, 39, 321)-net in base 32, using
- 1 times m-reduction [i] based on (17, 40, 321)-net in base 32, using
- base change [i] based on digital (2, 25, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 25, 321)-net over F256, using
(39−22, 39, 34357)-Net in Base 32 — Upper bound on s
There is no (17, 39, 34358)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 50219 687990 989592 954668 183886 953549 286456 199965 670573 941532 > 3239 [i]