Best Known (202−49, 202, s)-Nets in Base 4
(202−49, 202, 1032)-Net over F4 — Constructive and digital
Digital (153, 202, 1032)-net over F4, using
- 42 times duplication [i] based on digital (151, 200, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 50, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 50, 258)-net over F256, using
(202−49, 202, 2159)-Net over F4 — Digital
Digital (153, 202, 2159)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4202, 2159, F4, 49) (dual of [2159, 1957, 50]-code), using
- 1956 step Varšamov–Edel lengthening with (ri) = (14, 6, 3, 2, 2, 2, 1, 2, 1, 1, 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, 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, 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, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 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, 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, 9 times 0, 1, 10 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, 13 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, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 37 times 0, 1, 39 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 57 times 0, 1, 59 times 0) [i] based on linear OA(449, 50, F4, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,4)), using
- dual of repetition code with length 50 [i]
- 1956 step Varšamov–Edel lengthening with (ri) = (14, 6, 3, 2, 2, 2, 1, 2, 1, 1, 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, 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, 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, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 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, 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, 9 times 0, 1, 10 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, 13 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, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 37 times 0, 1, 39 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 57 times 0, 1, 59 times 0) [i] based on linear OA(449, 50, F4, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,4)), using
(202−49, 202, 360139)-Net in Base 4 — Upper bound on s
There is no (153, 202, 360140)-net in base 4, because
- 1 times m-reduction [i] would yield (153, 201, 360140)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10 329550 543240 143809 045510 066939 827594 254000 782350 396591 245981 214955 309707 361920 633548 847856 335816 269270 481711 282160 126716 > 4201 [i]