Best Known (128−30, 128, s)-Nets in Base 5
(128−30, 128, 460)-Net over F5 — Constructive and digital
Digital (98, 128, 460)-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 (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, 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, 40, 126)-net over F25, using
- digital (33, 48, 208)-net over F5, using
(128−30, 128, 3577)-Net over F5 — Digital
Digital (98, 128, 3577)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5128, 3577, F5, 30) (dual of [3577, 3449, 31]-code), using
- 444 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) [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
- 444 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) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
(128−30, 128, 1479951)-Net in Base 5 — Upper bound on s
There is no (98, 128, 1479952)-net in base 5, because
- 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]