Best Known (99, 99+118, s)-Nets in Base 4
(99, 99+118, 104)-Net over F4 — Constructive and digital
Digital (99, 217, 104)-net over F4, using
- t-expansion [i] based on digital (73, 217, 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+118, 144)-Net over F4 — Digital
Digital (99, 217, 144)-net over F4, using
- t-expansion [i] based on digital (91, 217, 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+118, 1198)-Net in Base 4 — Upper bound on s
There is no (99, 217, 1199)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 46061 298096 529637 269093 129664 814231 204019 686524 085666 056638 317955 792729 270125 128510 100755 873815 195765 318362 427175 702001 381587 329792 > 4217 [i]