Best Known (70, 91, s)-Nets in Base 5
(70, 91, 384)-Net over F5 — Constructive and digital
Digital (70, 91, 384)-net over F5, using
- 51 times duplication [i] based on digital (69, 90, 384)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (18, 28, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 14, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 14, 66)-net over F25, using
- digital (41, 62, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 31, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 31, 126)-net over F25, using
- digital (18, 28, 132)-net over F5, using
- (u, u+v)-construction [i] based on
(70, 91, 3398)-Net over F5 — Digital
Digital (70, 91, 3398)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(591, 3398, F5, 21) (dual of [3398, 3307, 22]-code), using
- 262 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) [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]
- 262 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) [i] based on linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using
(70, 91, 2211286)-Net in Base 5 — Upper bound on s
There is no (70, 91, 2211287)-net in base 5, because
- 1 times m-reduction [i] would yield (70, 90, 2211287)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 807 796106 713692 852219 464261 533730 858244 222641 299287 592403 742681 > 590 [i]