Best Known (87, 116, s)-Nets in Base 5
(87, 116, 400)-Net over F5 — Constructive and digital
Digital (87, 116, 400)-net over F5, using
- 8 times m-reduction [i] based on digital (87, 124, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 62, 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, 62, 200)-net over F25, using
(87, 116, 2572)-Net over F5 — Digital
Digital (87, 116, 2572)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5116, 2572, F5, 29) (dual of [2572, 2456, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(5116, 3125, F5, 29) (dual of [3125, 3009, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(5116, 3125, F5, 29) (dual of [3125, 3009, 30]-code), using
(87, 116, 833550)-Net in Base 5 — Upper bound on s
There is no (87, 116, 833551)-net in base 5, because
- 1 times m-reduction [i] would yield (87, 115, 833551)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 240 743707 359034 414377 088240 040238 724630 625475 941448 155100 589156 308446 211476 052425 > 5115 [i]