Best Known (95−21, 95, s)-Nets in Base 5
(95−21, 95, 400)-Net over F5 — Constructive and digital
Digital (74, 95, 400)-net over F5, using
- 3 times m-reduction [i] based on digital (74, 98, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 49, 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, 49, 200)-net over F25, using
(95−21, 95, 4359)-Net over F5 — Digital
Digital (74, 95, 4359)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(595, 4359, F5, 21) (dual of [4359, 4264, 22]-code), using
- 1219 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 40 times 0, 1, 66 times 0, 1, 104 times 0, 1, 155 times 0, 1, 213 times 0, 1, 269 times 0, 1, 316 times 0) [i] based on linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1219 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 23 times 0, 1, 40 times 0, 1, 66 times 0, 1, 104 times 0, 1, 155 times 0, 1, 213 times 0, 1, 269 times 0, 1, 316 times 0) [i] based on linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using
(95−21, 95, 4209530)-Net in Base 5 — Upper bound on s
There is no (74, 95, 4209531)-net in base 5, because
- 1 times m-reduction [i] would yield (74, 94, 4209531)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 504871 927743 786175 294275 118745 916350 400429 758114 092230 433364 613465 > 594 [i]