Best Known (72, 95, s)-Nets in Base 5
(72, 95, 356)-Net over F5 — Constructive and digital
Digital (72, 95, 356)-net over F5, using
- 51 times duplication [i] based on digital (71, 94, 356)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (17, 28, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 14, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- trace code for nets [i] based on digital (3, 14, 52)-net over F25, using
- digital (43, 66, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 33, 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, 33, 126)-net over F25, using
- digital (17, 28, 104)-net over F5, using
- (u, u+v)-construction [i] based on
(72, 95, 2904)-Net over F5 — Digital
Digital (72, 95, 2904)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(595, 2904, F5, 23) (dual of [2904, 2809, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(595, 3144, F5, 23) (dual of [3144, 3049, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(591, 3125, F5, 23) (dual of [3125, 3034, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(576, 3125, F5, 19) (dual of [3125, 3049, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(54, 19, F5, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,5)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(595, 3144, F5, 23) (dual of [3144, 3049, 24]-code), using
(72, 95, 1153367)-Net in Base 5 — Upper bound on s
There is no (72, 95, 1153368)-net in base 5, because
- 1 times m-reduction [i] would yield (72, 94, 1153368)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 504874 182285 354280 146108 731580 957900 548079 149938 964763 434106 844769 > 594 [i]