Best Known (110, 162, s)-Nets in Base 8
(110, 162, 1026)-Net over F8 — Constructive and digital
Digital (110, 162, 1026)-net over F8, using
- 2 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
(110, 162, 2122)-Net over F8 — Digital
Digital (110, 162, 2122)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8162, 2122, F8, 52) (dual of [2122, 1960, 53]-code), using
- 1959 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 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, 4 times 0, 1, 0, 0, 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, 7 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, 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, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 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, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 61 times 0, 1, 64 times 0, 1, 66 times 0, 1, 69 times 0, 1, 72 times 0, 1, 75 times 0, 1, 79 times 0, 1, 82 times 0) [i] based on linear OA(852, 53, F8, 52) (dual of [53, 1, 53]-code or 53-arc in PG(51,8)), using
- dual of repetition code with length 53 [i]
- 1959 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 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, 4 times 0, 1, 0, 0, 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, 7 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, 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, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 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, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 52 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 61 times 0, 1, 64 times 0, 1, 66 times 0, 1, 69 times 0, 1, 72 times 0, 1, 75 times 0, 1, 79 times 0, 1, 82 times 0) [i] based on linear OA(852, 53, F8, 52) (dual of [53, 1, 53]-code or 53-arc in PG(51,8)), using
(110, 162, 638453)-Net in Base 8 — Upper bound on s
There is no (110, 162, 638454)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 199 795954 507592 705066 451927 993006 193515 806566 491021 897895 066366 163865 943526 082436 395296 871121 241718 044187 062034 877589 112427 528112 078363 560684 064936 > 8162 [i]