Best Known (99, 99+110, s)-Nets in Base 4
(99, 99+110, 104)-Net over F4 — Constructive and digital
Digital (99, 209, 104)-net over F4, using
- t-expansion [i] based on digital (73, 209, 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
(99, 99+110, 144)-Net over F4 — Digital
Digital (99, 209, 144)-net over F4, using
- t-expansion [i] based on digital (91, 209, 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
(99, 99+110, 1335)-Net in Base 4 — Upper bound on s
There is no (99, 209, 1336)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 699408 335312 135899 678354 914866 199850 015702 047824 370768 106219 783597 658025 453507 611449 253804 072221 337995 745564 805337 980154 600855 > 4209 [i]