Best Known (234−53, 234, s)-Nets in Base 4
(234−53, 234, 1048)-Net over F4 — Constructive and digital
Digital (181, 234, 1048)-net over F4, using
- 42 times duplication [i] based on digital (179, 232, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 58, 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, 58, 262)-net over F256, using
(234−53, 234, 3478)-Net over F4 — Digital
Digital (181, 234, 3478)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4234, 3478, F4, 53) (dual of [3478, 3244, 54]-code), using
- 3243 step Varšamov–Edel lengthening with (ri) = (15, 6, 4, 2, 2, 2, 2, 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, 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, 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, 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, 6 times 0, 1, 5 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, 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, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 19 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, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 50 times 0, 1, 51 times 0, 1, 53 times 0, 1, 54 times 0, 1, 56 times 0, 1, 57 times 0, 1, 59 times 0, 1, 60 times 0, 1, 63 times 0, 1, 64 times 0, 1, 65 times 0, 1, 68 times 0, 1, 69 times 0, 1, 72 times 0, 1, 73 times 0, 1, 75 times 0, 1, 78 times 0, 1, 80 times 0, 1, 81 times 0, 1, 84 times 0, 1, 87 times 0, 1, 89 times 0) [i] based on linear OA(453, 54, F4, 53) (dual of [54, 1, 54]-code or 54-arc in PG(52,4)), using
- dual of repetition code with length 54 [i]
- 3243 step Varšamov–Edel lengthening with (ri) = (15, 6, 4, 2, 2, 2, 2, 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, 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, 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, 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, 6 times 0, 1, 5 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, 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, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 19 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, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 50 times 0, 1, 51 times 0, 1, 53 times 0, 1, 54 times 0, 1, 56 times 0, 1, 57 times 0, 1, 59 times 0, 1, 60 times 0, 1, 63 times 0, 1, 64 times 0, 1, 65 times 0, 1, 68 times 0, 1, 69 times 0, 1, 72 times 0, 1, 73 times 0, 1, 75 times 0, 1, 78 times 0, 1, 80 times 0, 1, 81 times 0, 1, 84 times 0, 1, 87 times 0, 1, 89 times 0) [i] based on linear OA(453, 54, F4, 53) (dual of [54, 1, 54]-code or 54-arc in PG(52,4)), using
(234−53, 234, 874067)-Net in Base 4 — Upper bound on s
There is no (181, 234, 874068)-net in base 4, because
- 1 times m-reduction [i] would yield (181, 233, 874068)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 190 538513 721541 660413 621837 143358 243646 520657 953903 129843 946551 855841 875839 209204 762842 931493 629266 278096 118683 321759 916915 963975 115564 267800 > 4233 [i]