Best Known (165−46, 165, s)-Nets in Base 8
(165−46, 165, 1026)-Net over F8 — Constructive and digital
Digital (119, 165, 1026)-net over F8, using
- t-expansion [i] based on digital (114, 165, 1026)-net over F8, using
- 7 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
- 7 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
(165−46, 165, 5180)-Net over F8 — Digital
Digital (119, 165, 5180)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8165, 5180, F8, 46) (dual of [5180, 5015, 47]-code), using
- 5014 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 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, 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, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 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, 24 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 62 times 0, 1, 65 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 82 times 0, 1, 87 times 0, 1, 90 times 0, 1, 95 times 0, 1, 99 times 0, 1, 104 times 0, 1, 110 times 0, 1, 114 times 0, 1, 120 times 0, 1, 126 times 0, 1, 131 times 0, 1, 138 times 0, 1, 145 times 0, 1, 152 times 0, 1, 159 times 0, 1, 166 times 0, 1, 175 times 0, 1, 183 times 0, 1, 191 times 0, 1, 201 times 0, 1, 210 times 0, 1, 221 times 0, 1, 231 times 0) [i] based on linear OA(846, 47, F8, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,8)), using
- dual of repetition code with length 47 [i]
- 5014 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 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, 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, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 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, 24 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 62 times 0, 1, 65 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 82 times 0, 1, 87 times 0, 1, 90 times 0, 1, 95 times 0, 1, 99 times 0, 1, 104 times 0, 1, 110 times 0, 1, 114 times 0, 1, 120 times 0, 1, 126 times 0, 1, 131 times 0, 1, 138 times 0, 1, 145 times 0, 1, 152 times 0, 1, 159 times 0, 1, 166 times 0, 1, 175 times 0, 1, 183 times 0, 1, 191 times 0, 1, 201 times 0, 1, 210 times 0, 1, 221 times 0, 1, 231 times 0) [i] based on linear OA(846, 47, F8, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,8)), using
(165−46, 165, 4055512)-Net in Base 8 — Upper bound on s
There is no (119, 165, 4055513)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 102293 733284 182686 076808 460451 540205 644990 663321 502552 511044 968134 541403 722115 375495 993047 770072 832205 613378 451764 328997 362071 240545 947898 341160 894184 > 8165 [i]