Best Known (125, 165, s)-Nets in Base 4
(125, 165, 1032)-Net over F4 — Constructive and digital
Digital (125, 165, 1032)-net over F4, using
- 41 times duplication [i] based on digital (124, 164, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 41, 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, 41, 258)-net over F256, using
(125, 165, 1829)-Net over F4 — Digital
Digital (125, 165, 1829)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4165, 1829, F4, 40) (dual of [1829, 1664, 41]-code), using
- 1663 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 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, 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, 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, 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 14 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, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 59 times 0, 1, 61 times 0) [i] based on linear OA(440, 41, F4, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,4)), using
- dual of repetition code with length 41 [i]
- 1663 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 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, 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, 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, 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 14 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, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 59 times 0, 1, 61 times 0) [i] based on linear OA(440, 41, F4, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,4)), using
(125, 165, 256538)-Net in Base 4 — Upper bound on s
There is no (125, 165, 256539)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2187 337343 700876 038684 898460 611728 795855 578526 921628 605808 018410 624588 339932 316618 932379 054515 741846 > 4165 [i]