Best Known (163−78, 163, s)-Nets in Base 4
(163−78, 163, 104)-Net over F4 — Constructive and digital
Digital (85, 163, 104)-net over F4, using
- t-expansion [i] based on digital (73, 163, 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
(163−78, 163, 138)-Net over F4 — Digital
Digital (85, 163, 138)-net over F4, using
(163−78, 163, 1653)-Net in Base 4 — Upper bound on s
There is no (85, 163, 1654)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 139 082484 522066 178588 440771 224902 622520 751081 395923 791875 019523 791622 808399 050570 419452 158003 072728 > 4163 [i]