Best Known (87, 87+26, s)-Nets in Base 5
(87, 87+26, 408)-Net over F5 — Constructive and digital
Digital (87, 113, 408)-net over F5, using
- 1 times m-reduction [i] based on digital (87, 114, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 57, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- trace code for nets [i] based on digital (30, 57, 204)-net over F25, using
(87, 87+26, 3718)-Net over F5 — Digital
Digital (87, 113, 3718)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5113, 3718, F5, 26) (dual of [3718, 3605, 27]-code), using
- 581 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 39 times 0, 1, 64 times 0, 1, 99 times 0, 1, 141 times 0, 1, 184 times 0) [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]
- 581 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 39 times 0, 1, 64 times 0, 1, 99 times 0, 1, 141 times 0, 1, 184 times 0) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
(87, 87+26, 1686576)-Net in Base 5 — Upper bound on s
There is no (87, 113, 1686577)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9 629656 394817 083532 497376 312639 328287 027918 582437 421093 779925 805299 461180 042325 > 5113 [i]