Best Known (101−34, 101, s)-Nets in Base 8
(101−34, 101, 371)-Net over F8 — Constructive and digital
Digital (67, 101, 371)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 19, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (48, 82, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 41, 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, 41, 177)-net over F64, using
- digital (2, 19, 17)-net over F8, using
(101−34, 101, 520)-Net in Base 8 — Constructive
(67, 101, 520)-net in base 8, using
- 1 times m-reduction [i] based on (67, 102, 520)-net in base 8, using
- trace code for nets [i] based on (16, 51, 260)-net in base 64, using
- 1 times m-reduction [i] based on (16, 52, 260)-net in base 64, using
- base change [i] based on digital (3, 39, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 39, 260)-net over F256, using
- 1 times m-reduction [i] based on (16, 52, 260)-net in base 64, using
- trace code for nets [i] based on (16, 51, 260)-net in base 64, using
(101−34, 101, 1109)-Net over F8 — Digital
Digital (67, 101, 1109)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8101, 1109, F8, 34) (dual of [1109, 1008, 35]-code), using
- 1007 step Varšamov–Edel lengthening with (ri) = (6, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 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, 0, 0, 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, 8 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, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 61 times 0, 1, 65 times 0) [i] based on linear OA(834, 35, F8, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,8)), using
- dual of repetition code with length 35 [i]
- 1007 step Varšamov–Edel lengthening with (ri) = (6, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 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, 0, 0, 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, 8 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, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 61 times 0, 1, 65 times 0) [i] based on linear OA(834, 35, F8, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,8)), using
(101−34, 101, 237818)-Net in Base 8 — Upper bound on s
There is no (67, 101, 237819)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 16 297208 861771 650460 326439 382330 716881 022237 532091 772937 411005 451037 692825 353700 175590 918710 > 8101 [i]