Best Known (149−41, 149, s)-Nets in Base 5
(149−41, 149, 408)-Net over F5 — Constructive and digital
Digital (108, 149, 408)-net over F5, using
- t-expansion [i] based on digital (105, 149, 408)-net over F5, using
- 1 times m-reduction [i] based on digital (105, 150, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 75, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- trace code for nets [i] based on digital (30, 75, 204)-net over F25, using
- 1 times m-reduction [i] based on digital (105, 150, 408)-net over F5, using
(149−41, 149, 1603)-Net over F5 — Digital
Digital (108, 149, 1603)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5149, 1603, F5, 41) (dual of [1603, 1454, 42]-code), using
- 1453 step Varšamov–Edel lengthening with (ri) = (10, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 55 times 0, 1, 58 times 0, 1, 61 times 0) [i] based on linear OA(541, 42, F5, 41) (dual of [42, 1, 42]-code or 42-arc in PG(40,5)), using
- dual of repetition code with length 42 [i]
- 1453 step Varšamov–Edel lengthening with (ri) = (10, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 55 times 0, 1, 58 times 0, 1, 61 times 0) [i] based on linear OA(541, 42, F5, 41) (dual of [42, 1, 42]-code or 42-arc in PG(40,5)), using
(149−41, 149, 308747)-Net in Base 5 — Upper bound on s
There is no (108, 149, 308748)-net in base 5, because
- 1 times m-reduction [i] would yield (108, 148, 308748)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 28 026326 455901 433046 450568 980713 527107 235766 045166 826753 893011 938702 620391 516841 154845 787778 618045 402881 > 5148 [i]