Best Known (64, 119, s)-Nets in Base 16
(64, 119, 522)-Net over F16 — Constructive and digital
Digital (64, 119, 522)-net over F16, using
- 1 times m-reduction [i] based on digital (64, 120, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 60, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 60, 261)-net over F256, using
(64, 119, 644)-Net over F16 — Digital
Digital (64, 119, 644)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(16119, 644, F16, 2, 55) (dual of [(644, 2), 1169, 56]-NRT-code), using
- 161 times duplication [i] based on linear OOA(16118, 644, F16, 2, 55) (dual of [(644, 2), 1170, 56]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(16114, 642, F16, 2, 55) (dual of [(642, 2), 1170, 56]-NRT-code), using
- extracting embedded OOA [i] based on digital (59, 114, 642)-net over F16, using
- trace code for nets [i] based on digital (2, 57, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- trace code for nets [i] based on digital (2, 57, 321)-net over F256, using
- extracting embedded OOA [i] based on digital (59, 114, 642)-net over F16, using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(16114, 642, F16, 2, 55) (dual of [(642, 2), 1170, 56]-NRT-code), using
- 161 times duplication [i] based on linear OOA(16118, 644, F16, 2, 55) (dual of [(644, 2), 1170, 56]-NRT-code), using
(64, 119, 133265)-Net in Base 16 — Upper bound on s
There is no (64, 119, 133266)-net in base 16, because
- 1 times m-reduction [i] would yield (64, 118, 133266)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 12195 682805 486255 327661 315002 602227 064645 713763 498421 697983 214690 219785 100160 136590 014622 438799 816327 672185 058455 092587 547881 134362 679399 291456 > 16118 [i]