Best Known (103−24, 103, s)-Nets in Base 5
(103−24, 103, 400)-Net over F5 — Constructive and digital
Digital (79, 103, 400)-net over F5, using
- 5 times m-reduction [i] based on digital (79, 108, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 54, 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, 54, 200)-net over F25, using
(103−24, 103, 3324)-Net over F5 — Digital
Digital (79, 103, 3324)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5103, 3324, F5, 24) (dual of [3324, 3221, 25]-code), using
- 187 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 10 times 0, 1, 23 times 0, 1, 49 times 0, 1, 94 times 0) [i] based on linear OA(596, 3130, F5, 24) (dual of [3130, 3034, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [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(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(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- 187 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 10 times 0, 1, 23 times 0, 1, 49 times 0, 1, 94 times 0) [i] based on linear OA(596, 3130, F5, 24) (dual of [3130, 3034, 25]-code), using
(103−24, 103, 1320660)-Net in Base 5 — Upper bound on s
There is no (79, 103, 1320661)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 986081 271261 995303 825185 934692 589215 280245 695803 675974 177937 415382 863825 > 5103 [i]