Best Known (103, 103+105, s)-Nets in Base 4
(103, 103+105, 104)-Net over F4 — Constructive and digital
Digital (103, 208, 104)-net over F4, using
- t-expansion [i] based on digital (73, 208, 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
(103, 103+105, 144)-Net over F4 — Digital
Digital (103, 208, 144)-net over F4, using
- t-expansion [i] based on digital (91, 208, 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
(103, 103+105, 1638)-Net in Base 4 — Upper bound on s
There is no (103, 208, 1639)-net in base 4, because
- 1 times m-reduction [i] would yield (103, 207, 1639)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 43535 140636 723272 291883 699543 407927 901596 065422 307503 430503 662227 107528 261265 636636 857548 007221 787754 757037 159321 114864 081780 > 4207 [i]