Best Known (112, 162, s)-Nets in Base 8
(112, 162, 1026)-Net over F8 — Constructive and digital
Digital (112, 162, 1026)-net over F8, using
- 6 times m-reduction [i] based on digital (112, 168, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 84, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 84, 513)-net over F64, using
(112, 162, 2667)-Net over F8 — Digital
Digital (112, 162, 2667)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8162, 2667, F8, 50) (dual of [2667, 2505, 51]-code), using
- 2504 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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, 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, 5 times 0, 1, 5 times 0, 1, 5 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, 14 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, 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, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 64 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 76 times 0, 1, 80 times 0, 1, 83 times 0, 1, 86 times 0, 1, 91 times 0, 1, 95 times 0, 1, 99 times 0, 1, 103 times 0, 1, 108 times 0) [i] based on linear OA(850, 51, F8, 50) (dual of [51, 1, 51]-code or 51-arc in PG(49,8)), using
- dual of repetition code with length 51 [i]
- 2504 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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, 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, 5 times 0, 1, 5 times 0, 1, 5 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, 14 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, 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, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 64 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 76 times 0, 1, 80 times 0, 1, 83 times 0, 1, 86 times 0, 1, 91 times 0, 1, 95 times 0, 1, 99 times 0, 1, 103 times 0, 1, 108 times 0) [i] based on linear OA(850, 51, F8, 50) (dual of [51, 1, 51]-code or 51-arc in PG(49,8)), using
(112, 162, 1034056)-Net in Base 8 — Upper bound on s
There is no (112, 162, 1034057)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 199 793239 348700 948196 188173 045138 224786 131019 352678 905813 162044 227815 675753 486337 034482 549626 243363 961439 186492 291406 988463 130691 553853 756872 286432 > 8162 [i]