Best Known (75, 101, s)-Nets in Base 5
(75, 101, 306)-Net over F5 — Constructive and digital
Digital (75, 101, 306)-net over F5, using
- 1 times m-reduction [i] based on digital (75, 102, 306)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (15, 28, 54)-net over F5, using
- trace code for nets [i] based on digital (1, 14, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- trace code for nets [i] based on digital (1, 14, 27)-net over F25, using
- digital (47, 74, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- digital (15, 28, 54)-net over F5, using
- (u, u+v)-construction [i] based on
(75, 101, 1986)-Net over F5 — Digital
Digital (75, 101, 1986)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5101, 1986, F5, 26) (dual of [1986, 1885, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
(75, 101, 381763)-Net in Base 5 — Upper bound on s
There is no (75, 101, 381764)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 39443 096823 451485 908673 865173 580462 437274 082371 455796 122995 431707 717009 > 5101 [i]