Best Known (111, 145, s)-Nets in Base 4
(111, 145, 1036)-Net over F4 — Constructive and digital
Digital (111, 145, 1036)-net over F4, using
- 41 times duplication [i] based on digital (110, 144, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 36, 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, 36, 259)-net over F256, using
(111, 145, 1956)-Net over F4 — Digital
Digital (111, 145, 1956)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4145, 1956, F4, 34) (dual of [1956, 1811, 35]-code), using
- 1810 step Varšamov–Edel lengthening with (ri) = (9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 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, 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, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 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, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0) [i] based on linear OA(434, 35, F4, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,4)), using
- dual of repetition code with length 35 [i]
- 1810 step Varšamov–Edel lengthening with (ri) = (9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 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, 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, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 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, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0) [i] based on linear OA(434, 35, F4, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,4)), using
(111, 145, 326605)-Net in Base 4 — Upper bound on s
There is no (111, 145, 326606)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1989 355694 078752 161148 877509 761244 772378 545456 439881 046155 553175 531264 014335 702561 851988 > 4145 [i]