Best Known (93, 93+43, s)-Nets in Base 8
(93, 93+43, 419)-Net over F8 — Constructive and digital
Digital (93, 136, 419)-net over F8, using
- 81 times duplication [i] based on digital (92, 135, 419)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 35, 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 (57, 100, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 50, 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, 50, 177)-net over F64, using
- digital (14, 35, 65)-net over F8, using
- (u, u+v)-construction [i] based on
(93, 93+43, 576)-Net in Base 8 — Constructive
(93, 136, 576)-net in base 8, using
- 10 times m-reduction [i] based on (93, 146, 576)-net in base 8, using
- trace code for nets [i] based on (20, 73, 288)-net in base 64, using
- 4 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
- 4 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- trace code for nets [i] based on (20, 73, 288)-net in base 64, using
(93, 93+43, 2003)-Net over F8 — Digital
Digital (93, 136, 2003)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8136, 2003, F8, 43) (dual of [2003, 1867, 44]-code), using
- 1866 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 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, 5 times 0, 1, 4 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, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 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, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 51 times 0, 1, 53 times 0, 1, 57 times 0, 1, 59 times 0, 1, 62 times 0, 1, 66 times 0, 1, 69 times 0, 1, 73 times 0, 1, 76 times 0, 1, 81 times 0, 1, 85 times 0, 1, 89 times 0, 1, 94 times 0) [i] based on linear OA(843, 44, F8, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,8)), using
- dual of repetition code with length 44 [i]
- 1866 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 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, 5 times 0, 1, 4 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, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 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, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 51 times 0, 1, 53 times 0, 1, 57 times 0, 1, 59 times 0, 1, 62 times 0, 1, 66 times 0, 1, 69 times 0, 1, 73 times 0, 1, 76 times 0, 1, 81 times 0, 1, 85 times 0, 1, 89 times 0, 1, 94 times 0) [i] based on linear OA(843, 44, F8, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,8)), using
(93, 93+43, 792439)-Net in Base 8 — Upper bound on s
There is no (93, 136, 792440)-net in base 8, because
- 1 times m-reduction [i] would yield (93, 135, 792440)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 82 633989 186126 519511 773468 226708 907564 431936 853792 572340 010774 127156 519217 564546 175398 993461 088554 949090 851951 025451 707849 > 8135 [i]