Best Known (190, 235, s)-Nets in Base 3
(190, 235, 896)-Net over F3 — Constructive and digital
Digital (190, 235, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (190, 236, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 59, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 59, 224)-net over F81, using
(190, 235, 3071)-Net over F3 — Digital
Digital (190, 235, 3071)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3235, 3071, F3, 45) (dual of [3071, 2836, 46]-code), using
- 2835 step Varšamov–Edel lengthening with (ri) = (16, 7, 5, 3, 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, 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, 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, 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, 5 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, 7 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, 10 times 0, 1, 11 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, 13 times 0, 1, 13 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, 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, 24 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, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 33 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, 41 times 0, 1, 41 times 0, 1, 43 times 0, 1, 43 times 0, 1, 45 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 49 times 0, 1, 51 times 0, 1, 53 times 0, 1, 53 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, 64 times 0, 1, 66 times 0, 1, 68 times 0, 1, 69 times 0, 1, 71 times 0, 1, 74 times 0) [i] based on linear OA(345, 46, F3, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,3)), using
- dual of repetition code with length 46 [i]
- 2835 step Varšamov–Edel lengthening with (ri) = (16, 7, 5, 3, 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, 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, 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, 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, 5 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, 7 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, 10 times 0, 1, 11 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, 13 times 0, 1, 13 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, 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, 24 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, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 33 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, 41 times 0, 1, 41 times 0, 1, 43 times 0, 1, 43 times 0, 1, 45 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 49 times 0, 1, 51 times 0, 1, 53 times 0, 1, 53 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, 64 times 0, 1, 66 times 0, 1, 68 times 0, 1, 69 times 0, 1, 71 times 0, 1, 74 times 0) [i] based on linear OA(345, 46, F3, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,3)), using
(190, 235, 537824)-Net in Base 3 — Upper bound on s
There is no (190, 235, 537825)-net in base 3, because
- 1 times m-reduction [i] would yield (190, 234, 537825)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 4429 726736 113161 141225 924737 100140 727167 660992 640676 382982 465549 698502 959692 540518 490575 252407 978130 594979 759321 > 3234 [i]