Best Known (187, 242, s)-Nets in Base 4
(187, 242, 1048)-Net over F4 — Constructive and digital
Digital (187, 242, 1048)-net over F4, using
- 42 times duplication [i] based on digital (185, 240, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 60, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 60, 262)-net over F256, using
(187, 242, 3515)-Net over F4 — Digital
Digital (187, 242, 3515)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4242, 3515, F4, 55) (dual of [3515, 3273, 56]-code), using
- 3272 step Varšamov–Edel lengthening with (ri) = (15, 7, 4, 2, 2, 2, 2, 1, 1, 1, 1, 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, 1, 0, 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, 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, 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, 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, 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, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 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, 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, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 30 times 0, 1, 32 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 54 times 0, 1, 55 times 0, 1, 57 times 0, 1, 58 times 0, 1, 60 times 0, 1, 61 times 0, 1, 63 times 0, 1, 65 times 0, 1, 66 times 0, 1, 68 times 0, 1, 70 times 0, 1, 72 times 0, 1, 74 times 0, 1, 76 times 0, 1, 77 times 0, 1, 80 times 0, 1, 82 times 0, 1, 84 times 0, 1, 87 times 0) [i] based on linear OA(455, 56, F4, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,4)), using
- dual of repetition code with length 56 [i]
- 3272 step Varšamov–Edel lengthening with (ri) = (15, 7, 4, 2, 2, 2, 2, 1, 1, 1, 1, 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, 1, 0, 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, 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, 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, 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, 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, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 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, 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, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 30 times 0, 1, 32 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 54 times 0, 1, 55 times 0, 1, 57 times 0, 1, 58 times 0, 1, 60 times 0, 1, 61 times 0, 1, 63 times 0, 1, 65 times 0, 1, 66 times 0, 1, 68 times 0, 1, 70 times 0, 1, 72 times 0, 1, 74 times 0, 1, 76 times 0, 1, 77 times 0, 1, 80 times 0, 1, 82 times 0, 1, 84 times 0, 1, 87 times 0) [i] based on linear OA(455, 56, F4, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,4)), using
(187, 242, 861424)-Net in Base 4 — Upper bound on s
There is no (187, 242, 861425)-net in base 4, because
- 1 times m-reduction [i] would yield (187, 241, 861425)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 487119 903710 026171 017460 751749 690159 350702 203394 983420 106737 878352 146973 241980 921879 785911 833031 862353 905018 699720 507849 426044 278997 740323 342752 > 4241 [i]