Best Known (190−45, 190, s)-Nets in Base 4
(190−45, 190, 1036)-Net over F4 — Constructive and digital
Digital (145, 190, 1036)-net over F4, using
- 42 times duplication [i] based on digital (143, 188, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 47, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 47, 259)-net over F256, using
(190−45, 190, 2311)-Net over F4 — Digital
Digital (145, 190, 2311)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4190, 2311, F4, 45) (dual of [2311, 2121, 46]-code), using
- 2120 step Varšamov–Edel lengthening with (ri) = (12, 6, 3, 3, 2, 1, 1, 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, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 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, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 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, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 48 times 0, 1, 50 times 0, 1, 52 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 58 times 0, 1, 61 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 69 times 0) [i] based on linear OA(445, 46, F4, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,4)), using
- dual of repetition code with length 46 [i]
- 2120 step Varšamov–Edel lengthening with (ri) = (12, 6, 3, 3, 2, 1, 1, 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, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 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, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 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, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 48 times 0, 1, 50 times 0, 1, 52 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 58 times 0, 1, 61 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 69 times 0) [i] based on linear OA(445, 46, F4, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,4)), using
(190−45, 190, 448701)-Net in Base 4 — Upper bound on s
There is no (145, 190, 448702)-net in base 4, because
- 1 times m-reduction [i] would yield (145, 189, 448702)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 615682 558578 458757 356171 631831 653795 893160 153073 144814 741825 139568 369874 425518 761272 317318 853729 740898 748827 343180 > 4189 [i]