Best Known (163, 163+96, s)-Nets in Base 4
(163, 163+96, 200)-Net over F4 — Constructive and digital
Digital (163, 259, 200)-net over F4, using
- t-expansion [i] based on digital (161, 259, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 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) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(163, 163+96, 475)-Net over F4 — Digital
Digital (163, 259, 475)-net over F4, using
(163, 163+96, 11034)-Net in Base 4 — Upper bound on s
There is no (163, 259, 11035)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 861724 081480 578887 699850 535913 453241 012467 691027 787134 166778 654172 124289 782607 882807 603461 094814 057314 517605 104306 606117 792470 294318 630427 169398 629503 597128 > 4259 [i]