Best Known (129−31, 129, s)-Nets in Base 5
(129−31, 129, 416)-Net over F5 — Constructive and digital
Digital (98, 129, 416)-net over F5, using
- 51 times duplication [i] based on digital (97, 128, 416)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (33, 48, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 24, 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, 24, 104)-net over F25, using
- digital (49, 80, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 40, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- trace code for nets [i] based on digital (9, 40, 104)-net over F25, using
- digital (33, 48, 208)-net over F5, using
- (u, u+v)-construction [i] based on
(129−31, 129, 3254)-Net over F5 — Digital
Digital (98, 129, 3254)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5129, 3254, F5, 31) (dual of [3254, 3125, 32]-code), using
- 120 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 32 times 0, 1, 54 times 0) [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]
- 120 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 32 times 0, 1, 54 times 0) [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
(129−31, 129, 1479951)-Net in Base 5 — Upper bound on s
There is no (98, 129, 1479952)-net in base 5, because
- 1 times m-reduction [i] would yield (98, 128, 1479952)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 293874 583548 908092 404478 161891 292481 907558 196753 755325 188455 128770 454029 587827 612418 350145 > 5128 [i]