Best Known (100, 209, s)-Nets in Base 4
(100, 209, 104)-Net over F4 — Constructive and digital
Digital (100, 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
(100, 209, 144)-Net over F4 — Digital
Digital (100, 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
(100, 209, 1413)-Net in Base 4 — Upper bound on s
There is no (100, 209, 1414)-net in base 4, because
- 1 times m-reduction [i] would yield (100, 208, 1414)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 175370 717784 046281 295240 239205 051288 134277 926320 083804 257017 383536 114798 364471 905725 939043 850030 796094 638341 234480 374453 543040 > 4208 [i]