Best Known (65, 65+30, s)-Nets in Base 8
(65, 65+30, 382)-Net over F8 — Constructive and digital
Digital (65, 95, 382)-net over F8, using
- 1 times m-reduction [i] based on digital (65, 96, 382)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 20, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (45, 76, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 38, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 38, 177)-net over F64, using
- digital (5, 20, 28)-net over F8, using
- (u, u+v)-construction [i] based on
(65, 65+30, 576)-Net in Base 8 — Constructive
(65, 95, 576)-net in base 8, using
- 3 times m-reduction [i] based on (65, 98, 576)-net in base 8, using
- trace code for nets [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- trace code for nets [i] based on (16, 49, 288)-net in base 64, using
(65, 65+30, 1530)-Net over F8 — Digital
Digital (65, 95, 1530)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(895, 1530, F8, 30) (dual of [1530, 1435, 31]-code), using
- 1434 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 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, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 34 times 0, 1, 37 times 0, 1, 39 times 0, 1, 42 times 0, 1, 46 times 0, 1, 49 times 0, 1, 53 times 0, 1, 57 times 0, 1, 62 times 0, 1, 66 times 0, 1, 71 times 0, 1, 77 times 0, 1, 82 times 0, 1, 89 times 0, 1, 96 times 0, 1, 103 times 0) [i] based on linear OA(830, 31, F8, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,8)), using
- dual of repetition code with length 31 [i]
- 1434 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 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, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 34 times 0, 1, 37 times 0, 1, 39 times 0, 1, 42 times 0, 1, 46 times 0, 1, 49 times 0, 1, 53 times 0, 1, 57 times 0, 1, 62 times 0, 1, 66 times 0, 1, 71 times 0, 1, 77 times 0, 1, 82 times 0, 1, 89 times 0, 1, 96 times 0, 1, 103 times 0) [i] based on linear OA(830, 31, F8, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,8)), using
(65, 65+30, 481094)-Net in Base 8 — Upper bound on s
There is no (65, 95, 481095)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 62 166646 238052 498691 588150 639281 764020 035626 504149 832380 426674 178067 259024 907433 909120 > 895 [i]