Best Known (111, 111+61, s)-Nets in Base 8
(111, 111+61, 382)-Net over F8 — Constructive and digital
Digital (111, 172, 382)-net over F8, using
- 81 times duplication [i] based on digital (110, 171, 382)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 35, 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 (75, 136, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 68, 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, 68, 177)-net over F64, using
- digital (5, 35, 28)-net over F8, using
- (u, u+v)-construction [i] based on
(111, 111+61, 576)-Net in Base 8 — Constructive
(111, 172, 576)-net in base 8, using
- t-expansion [i] based on (108, 172, 576)-net in base 8, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
- 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 78, 288)-net over F128, using
- 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
(111, 111+61, 1316)-Net over F8 — Digital
Digital (111, 172, 1316)-net over F8, using
(111, 111+61, 241696)-Net in Base 8 — Upper bound on s
There is no (111, 172, 241697)-net in base 8, because
- 1 times m-reduction [i] would yield (111, 171, 241697)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 26818 316658 338416 074205 227210 294066 339155 849926 855447 268621 426395 670455 061485 952735 264863 610361 528215 485711 463865 168994 777305 925591 559352 731027 488927 481072 > 8171 [i]