Best Known (72, 96, s)-Nets in Base 5
(72, 96, 312)-Net over F5 — Constructive and digital
Digital (72, 96, 312)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (18, 30, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 15, 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, 15, 52)-net over F25, using
- digital (42, 66, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 33, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- trace code for nets [i] based on digital (9, 33, 104)-net over F25, using
- digital (18, 30, 104)-net over F5, using
(72, 96, 2346)-Net over F5 — Digital
Digital (72, 96, 2346)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(596, 2346, F5, 24) (dual of [2346, 2250, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(596, 3125, F5, 24) (dual of [3125, 3029, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(596, 3125, F5, 24) (dual of [3125, 3029, 25]-code), using
(72, 96, 516480)-Net in Base 5 — Upper bound on s
There is no (72, 96, 516481)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 12 621788 383505 924388 201239 931240 575635 569078 805679 241139 972525 587025 > 596 [i]