Best Known (101, 101+108, s)-Nets in Base 4
(101, 101+108, 104)-Net over F4 — Constructive and digital
Digital (101, 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
(101, 101+108, 144)-Net over F4 — Digital
Digital (101, 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
(101, 101+108, 1450)-Net in Base 4 — Upper bound on s
There is no (101, 209, 1451)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 679008 216138 146399 498662 755295 534315 051978 649174 314417 068860 327342 843549 929150 506129 151371 107763 501169 321136 070165 515182 621360 > 4209 [i]