Best Known (245−60, 245, s)-Nets in Base 4
(245−60, 245, 1032)-Net over F4 — Constructive and digital
Digital (185, 245, 1032)-net over F4, using
- 41 times duplication [i] based on digital (184, 244, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 61, 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, 61, 258)-net over F256, using
(245−60, 245, 2436)-Net over F4 — Digital
Digital (185, 245, 2436)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4245, 2436, F4, 60) (dual of [2436, 2191, 61]-code), using
- 2190 step Varšamov–Edel lengthening with (ri) = (16, 7, 4, 3, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 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, 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, 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, 4 times 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, 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, 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, 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, 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, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 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, 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, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 27 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 30 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 38 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 48 times 0, 1, 49 times 0, 1, 50 times 0, 1, 51 times 0, 1, 53 times 0, 1, 54 times 0) [i] based on linear OA(460, 61, F4, 60) (dual of [61, 1, 61]-code or 61-arc in PG(59,4)), using
- dual of repetition code with length 61 [i]
- 2190 step Varšamov–Edel lengthening with (ri) = (16, 7, 4, 3, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 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, 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, 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, 4 times 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, 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, 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, 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, 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, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 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, 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, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 27 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 30 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 38 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 48 times 0, 1, 49 times 0, 1, 50 times 0, 1, 51 times 0, 1, 53 times 0, 1, 54 times 0) [i] based on linear OA(460, 61, F4, 60) (dual of [61, 1, 61]-code or 61-arc in PG(59,4)), using
(245−60, 245, 331480)-Net in Base 4 — Upper bound on s
There is no (185, 245, 331481)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3196 683831 310418 937636 448093 920322 130355 165460 460765 279742 694072 895453 797257 557968 215249 707874 382989 633732 972459 171002 443346 199452 649570 137293 097632 > 4245 [i]