Best Known (118, 118+48, s)-Nets in Base 8
(118, 118+48, 1026)-Net over F8 — Constructive and digital
Digital (118, 166, 1026)-net over F8, using
- t-expansion [i] based on digital (114, 166, 1026)-net over F8, using
- 6 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 86, 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, 86, 513)-net over F64, using
- 6 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
(118, 118+48, 4085)-Net over F8 — Digital
Digital (118, 166, 4085)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8166, 4085, F8, 48) (dual of [4085, 3919, 49]-code), using
- 3918 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 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, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 7 times 0, 1, 6 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, 10 times 0, 1, 10 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, 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, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 77 times 0, 1, 81 times 0, 1, 84 times 0, 1, 89 times 0, 1, 92 times 0, 1, 97 times 0, 1, 102 times 0, 1, 106 times 0, 1, 111 times 0, 1, 116 times 0, 1, 121 times 0, 1, 127 times 0, 1, 133 times 0, 1, 139 times 0, 1, 145 times 0, 1, 152 times 0, 1, 159 times 0, 1, 166 times 0, 1, 174 times 0) [i] based on linear OA(848, 49, F8, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,8)), using
- dual of repetition code with length 49 [i]
- 3918 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 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, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 7 times 0, 1, 6 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, 10 times 0, 1, 10 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, 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, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 61 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 77 times 0, 1, 81 times 0, 1, 84 times 0, 1, 89 times 0, 1, 92 times 0, 1, 97 times 0, 1, 102 times 0, 1, 106 times 0, 1, 111 times 0, 1, 116 times 0, 1, 121 times 0, 1, 127 times 0, 1, 133 times 0, 1, 139 times 0, 1, 145 times 0, 1, 152 times 0, 1, 159 times 0, 1, 166 times 0, 1, 174 times 0) [i] based on linear OA(848, 49, F8, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,8)), using
(118, 118+48, 2469644)-Net in Base 8 — Upper bound on s
There is no (118, 166, 2469645)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 818349 862604 473662 796561 929841 129144 963617 083863 631731 461924 159929 431957 117662 553923 860664 356388 675055 012266 798145 418245 583936 753100 827165 055520 020688 > 8166 [i]