Best Known (119−36, 119, s)-Nets in Base 8
(119−36, 119, 419)-Net over F8 — Constructive and digital
Digital (83, 119, 419)-net over F8, using
- 1 times m-reduction [i] based on digital (83, 120, 419)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 32, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (51, 88, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 44, 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, 44, 177)-net over F64, using
- digital (14, 32, 65)-net over F8, using
- (u, u+v)-construction [i] based on
(119−36, 119, 576)-Net in Base 8 — Constructive
(83, 119, 576)-net in base 8, using
- t-expansion [i] based on (81, 119, 576)-net in base 8, using
- 7 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 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, 54, 288)-net over F128, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- 7 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
(119−36, 119, 2355)-Net over F8 — Digital
Digital (83, 119, 2355)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8119, 2355, F8, 36) (dual of [2355, 2236, 37]-code), using
- 2235 step Varšamov–Edel lengthening with (ri) = (6, 3, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 35 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 45 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 60 times 0, 1, 64 times 0, 1, 68 times 0, 1, 73 times 0, 1, 77 times 0, 1, 81 times 0, 1, 87 times 0, 1, 93 times 0, 1, 98 times 0, 1, 104 times 0, 1, 111 times 0, 1, 118 times 0, 1, 125 times 0, 1, 133 times 0) [i] based on linear OA(836, 37, F8, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,8)), using
- dual of repetition code with length 37 [i]
- 2235 step Varšamov–Edel lengthening with (ri) = (6, 3, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 35 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 45 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 60 times 0, 1, 64 times 0, 1, 68 times 0, 1, 73 times 0, 1, 77 times 0, 1, 81 times 0, 1, 87 times 0, 1, 93 times 0, 1, 98 times 0, 1, 104 times 0, 1, 111 times 0, 1, 118 times 0, 1, 125 times 0, 1, 133 times 0) [i] based on linear OA(836, 37, F8, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,8)), using
(119−36, 119, 1007988)-Net in Base 8 — Upper bound on s
There is no (83, 119, 1007989)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 293571 459274 334712 738007 908307 694264 646081 201803 718136 768732 364465 322983 271036 543038 681819 746421 156899 400890 > 8119 [i]