Best Known (108, 108+35, s)-Nets in Base 5
(108, 108+35, 460)-Net over F5 — Constructive and digital
Digital (108, 143, 460)-net over F5, using
- 51 times duplication [i] based on digital (107, 142, 460)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (35, 52, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 26, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- trace code for nets [i] based on digital (9, 26, 104)-net over F25, using
- digital (55, 90, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 45, 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, 45, 126)-net over F25, using
- digital (35, 52, 208)-net over F5, using
- (u, u+v)-construction [i] based on
(108, 108+35, 3149)-Net over F5 — Digital
Digital (108, 143, 3149)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5143, 3149, F5, 35) (dual of [3149, 3006, 36]-code), using
- 22 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 17 times 0) [i] based on linear OA(5140, 3124, F5, 35) (dual of [3124, 2984, 36]-code), using
- 1 times truncation [i] based on linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 1 times truncation [i] based on linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using
- 22 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 17 times 0) [i] based on linear OA(5140, 3124, F5, 35) (dual of [3124, 2984, 36]-code), using
(108, 108+35, 1236904)-Net in Base 5 — Upper bound on s
There is no (108, 143, 1236905)-net in base 5, because
- 1 times m-reduction [i] would yield (108, 142, 1236905)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1793 669084 912323 350261 667683 131757 322362 046253 700752 495467 627223 994944 759331 979652 375414 839202 526565 > 5142 [i]