Best Known (160−50, 160, s)-Nets in Base 8
(160−50, 160, 1026)-Net over F8 — Constructive and digital
Digital (110, 160, 1026)-net over F8, using
- 4 times m-reduction [i] based on digital (110, 164, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 82, 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, 82, 513)-net over F64, using
(160−50, 160, 2452)-Net over F8 — Digital
Digital (110, 160, 2452)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8160, 2452, F8, 50) (dual of [2452, 2292, 51]-code), using
- 2291 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) [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]
- 2291 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) [i] based on linear OA(850, 51, F8, 50) (dual of [51, 1, 51]-code or 51-arc in PG(49,8)), using
(160−50, 160, 875580)-Net in Base 8 — Upper bound on s
There is no (110, 160, 875581)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 121811 159813 019967 535329 227679 733092 971400 158200 617567 220875 246775 018540 827210 611351 412155 918633 536232 256732 973388 682914 753495 649261 779660 159044 > 8160 [i]