Best Known (97−24, 97, s)-Nets in Base 5
(97−24, 97, 312)-Net over F5 — Constructive and digital
Digital (73, 97, 312)-net over F5, using
- 1 times m-reduction [i] based on digital (73, 98, 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 (43, 68, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 34, 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, 34, 104)-net over F25, using
- digital (18, 30, 104)-net over F5, using
- (u, u+v)-construction [i] based on
(97−24, 97, 2525)-Net over F5 — Digital
Digital (73, 97, 2525)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(597, 2525, F5, 24) (dual of [2525, 2428, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(597, 3136, F5, 24) (dual of [3136, 3039, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] 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]
- linear OA(586, 3125, F5, 22) (dual of [3125, 3039, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(597, 3136, F5, 24) (dual of [3136, 3039, 25]-code), using
(97−24, 97, 590612)-Net in Base 5 — Upper bound on s
There is no (73, 97, 590613)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 63 109386 516925 237093 320168 059437 042120 872000 495273 584347 140140 546001 > 597 [i]