Best Known (68, 68+61, s)-Nets in Base 16
(68, 68+61, 520)-Net over F16 — Constructive and digital
Digital (68, 129, 520)-net over F16, using
- 1 times m-reduction [i] based on digital (68, 130, 520)-net over F16, using
- trace code for nets [i] based on digital (3, 65, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 65, 260)-net over F256, using
(68, 68+61, 642)-Net over F16 — Digital
Digital (68, 129, 642)-net over F16, using
- t-expansion [i] based on digital (67, 129, 642)-net over F16, using
- 1 times m-reduction [i] based on digital (67, 130, 642)-net over F16, using
- trace code for nets [i] based on digital (2, 65, 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, 65, 321)-net over F256, using
- 1 times m-reduction [i] based on digital (67, 130, 642)-net over F16, using
(68, 68+61, 110207)-Net in Base 16 — Upper bound on s
There is no (68, 129, 110208)-net in base 16, because
- 1 times m-reduction [i] would yield (68, 128, 110208)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 13409 782909 683514 287247 879805 699547 959954 521897 703948 398645 481619 431007 525012 024506 880843 238853 492104 016929 528849 301485 565636 851808 830289 833187 561677 104601 > 16128 [i]