Best Known (108, 144, s)-Nets in Base 5
(108, 144, 418)-Net over F5 — Constructive and digital
Digital (108, 144, 418)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 18)-net over F5, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 4 and N(F) ≥ 18, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- digital (86, 122, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 61, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- trace code for nets [i] based on digital (25, 61, 200)-net over F25, using
- digital (4, 22, 18)-net over F5, using
(108, 144, 2922)-Net over F5 — Digital
Digital (108, 144, 2922)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 2922, F5, 36) (dual of [2922, 2778, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 3138, F5, 36) (dual of [3138, 2994, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [i] based on
- linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(5131, 3125, F5, 33) (dual of [3125, 2994, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(53, 13, F5, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(5144, 3138, F5, 36) (dual of [3138, 2994, 37]-code), using
(108, 144, 737602)-Net in Base 5 — Upper bound on s
There is no (108, 144, 737603)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 44841 975641 076899 245257 722027 933065 672931 203840 377353 985497 592508 440029 852363 296590 825121 876135 136825 > 5144 [i]