Best Known (104−25, 104, s)-Nets in Base 5
(104−25, 104, 400)-Net over F5 — Constructive and digital
Digital (79, 104, 400)-net over F5, using
- 4 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
(104−25, 104, 3147)-Net over F5 — Digital
Digital (79, 104, 3147)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5104, 3147, F5, 25) (dual of [3147, 3043, 26]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0) [i] based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
- 1 times truncation [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 1 times truncation [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 11 times 0) [i] based on linear OA(5100, 3124, F5, 25) (dual of [3124, 3024, 26]-code), using
(104−25, 104, 1320660)-Net in Base 5 — Upper bound on s
There is no (79, 104, 1320661)-net in base 5, because
- 1 times m-reduction [i] would yield (79, 103, 1320661)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 986081 271261 995303 825185 934692 589215 280245 695803 675974 177937 415382 863825 > 5103 [i]