Best Known (113−42, 113, s)-Nets in Base 8
(113−42, 113, 354)-Net over F8 — Constructive and digital
Digital (71, 113, 354)-net over F8, using
- 15 times m-reduction [i] based on digital (71, 128, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 64, 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, 64, 177)-net over F64, using
(113−42, 113, 514)-Net in Base 8 — Constructive
(71, 113, 514)-net in base 8, using
- 81 times duplication [i] based on (70, 112, 514)-net in base 8, using
- base change [i] based on digital (42, 84, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 42, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 42, 257)-net over F256, using
- base change [i] based on digital (42, 84, 514)-net over F16, using
(113−42, 113, 731)-Net over F8 — Digital
Digital (71, 113, 731)-net over F8, using
(113−42, 113, 89704)-Net in Base 8 — Upper bound on s
There is no (71, 113, 89705)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1 119917 746596 544294 098756 316257 464855 278270 562507 501348 368267 009653 508156 894898 131983 433370 992612 852336 > 8113 [i]