Best Known (130−30, 130, s)-Nets in Base 5
(130−30, 130, 504)-Net over F5 — Constructive and digital
Digital (100, 130, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (35, 50, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 25, 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, 25, 126)-net over F25, using
- digital (50, 80, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 40, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- trace code for nets [i] based on digital (10, 40, 126)-net over F25, using
- digital (35, 50, 252)-net over F5, using
(130−30, 130, 3982)-Net over F5 — Digital
Digital (100, 130, 3982)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5130, 3982, F5, 30) (dual of [3982, 3852, 31]-code), using
- 847 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 42 times 0, 1, 78 times 0, 1, 124 times 0, 1, 164 times 0, 1, 191 times 0, 1, 210 times 0) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
- 1 times truncation [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- 847 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 42 times 0, 1, 78 times 0, 1, 124 times 0, 1, 164 times 0, 1, 191 times 0, 1, 210 times 0) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
(130−30, 130, 1834189)-Net in Base 5 — Upper bound on s
There is no (100, 130, 1834190)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 7 346885 290237 140240 859025 937346 389789 208475 357663 416309 160788 506719 789631 292800 568752 463705 > 5130 [i]