Best Known (101, 216, s)-Nets in Base 4
(101, 216, 104)-Net over F4 — Constructive and digital
Digital (101, 216, 104)-net over F4, using
- t-expansion [i] based on digital (73, 216, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(101, 216, 144)-Net over F4 — Digital
Digital (101, 216, 144)-net over F4, using
- t-expansion [i] based on digital (91, 216, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(101, 216, 1327)-Net in Base 4 — Upper bound on s
There is no (101, 216, 1328)-net in base 4, because
- 1 times m-reduction [i] would yield (101, 215, 1328)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2887 718770 648593 050605 070540 785414 136351 231239 858707 323890 192593 731328 639280 320178 804861 571509 294028 337987 247206 006540 510061 370320 > 4215 [i]