Best Known (120, 120+47, s)-Nets in Base 8
(120, 120+47, 1026)-Net over F8 — Constructive and digital
Digital (120, 167, 1026)-net over F8, using
- t-expansion [i] based on digital (114, 167, 1026)-net over F8, using
- 5 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
- 5 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
(120, 120+47, 4907)-Net over F8 — Digital
Digital (120, 167, 4907)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8167, 4907, F8, 47) (dual of [4907, 4740, 48]-code), using
- 4739 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 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, 5 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, 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, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 21 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, 34 times 0, 1, 35 times 0, 1, 36 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, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 77 times 0, 1, 82 times 0, 1, 85 times 0, 1, 90 times 0, 1, 93 times 0, 1, 99 times 0, 1, 102 times 0, 1, 108 times 0, 1, 112 times 0, 1, 118 times 0, 1, 124 times 0, 1, 129 times 0, 1, 135 times 0, 1, 142 times 0, 1, 149 times 0, 1, 155 times 0, 1, 162 times 0, 1, 171 times 0, 1, 178 times 0, 1, 186 times 0, 1, 195 times 0, 1, 205 times 0, 1, 214 times 0) [i] based on linear OA(847, 48, F8, 47) (dual of [48, 1, 48]-code or 48-arc in PG(46,8)), using
- dual of repetition code with length 48 [i]
- 4739 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 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, 5 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, 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, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 21 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, 34 times 0, 1, 35 times 0, 1, 36 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, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 77 times 0, 1, 82 times 0, 1, 85 times 0, 1, 90 times 0, 1, 93 times 0, 1, 99 times 0, 1, 102 times 0, 1, 108 times 0, 1, 112 times 0, 1, 118 times 0, 1, 124 times 0, 1, 129 times 0, 1, 135 times 0, 1, 142 times 0, 1, 149 times 0, 1, 155 times 0, 1, 162 times 0, 1, 171 times 0, 1, 178 times 0, 1, 186 times 0, 1, 195 times 0, 1, 205 times 0, 1, 214 times 0) [i] based on linear OA(847, 48, F8, 47) (dual of [48, 1, 48]-code or 48-arc in PG(46,8)), using
(120, 120+47, 4439260)-Net in Base 8 — Upper bound on s
There is no (120, 167, 4439261)-net in base 8, because
- 1 times m-reduction [i] would yield (120, 166, 4439261)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 818348 450664 091374 612816 374829 663082 591218 564314 498690 681315 309661 355446 978188 216005 714249 191000 441853 864774 247298 943511 479192 537684 405501 416730 961368 > 8166 [i]