Best Known (111−26, 111, s)-Nets in Base 5
(111−26, 111, 400)-Net over F5 — Constructive and digital
Digital (85, 111, 400)-net over F5, using
- 9 times m-reduction [i] based on digital (85, 120, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 60, 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, 60, 200)-net over F25, using
(111−26, 111, 3389)-Net over F5 — Digital
Digital (85, 111, 3389)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5111, 3389, F5, 26) (dual of [3389, 3278, 27]-code), using
- 254 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) [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]
- 254 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) [i] based on linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using
(111−26, 111, 1316653)-Net in Base 5 — Upper bound on s
There is no (85, 111, 1316654)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 385186 317638 947294 329378 042602 938570 782468 742471 941846 860960 620719 099057 700665 > 5111 [i]