Best Known (206−123, 206, s)-Nets in Base 4
(206−123, 206, 104)-Net over F4 — Constructive and digital
Digital (83, 206, 104)-net over F4, using
- t-expansion [i] based on digital (73, 206, 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
(206−123, 206, 129)-Net over F4 — Digital
Digital (83, 206, 129)-net over F4, using
- t-expansion [i] based on digital (81, 206, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(206−123, 206, 779)-Net in Base 4 — Upper bound on s
There is no (83, 206, 780)-net in base 4, because
- 1 times m-reduction [i] would yield (83, 205, 780)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2736 394309 345786 424575 676634 073999 159403 879236 163059 932426 136591 651207 092628 765226 579982 132422 411198 529856 663033 485425 786560 > 4205 [i]