Best Known (186−160, 186, s)-Nets in Base 4
(186−160, 186, 34)-Net over F4 — Constructive and digital
Digital (26, 186, 34)-net over F4, using
- t-expansion [i] based on digital (21, 186, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(186−160, 186, 36)-Net in Base 4 — Constructive
(26, 186, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
(186−160, 186, 55)-Net over F4 — Digital
Digital (26, 186, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
(186−160, 186, 94)-Net in Base 4 — Upper bound on s
There is no (26, 186, 95)-net in base 4, because
- extracting embedded OOA [i] would yield OOA(4186, 95, S4, 2, 160), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 693054 953751 325278 652615 004303 045905 687020 046777 812161 513403 232213 683357 369020 768459 206753 139586 218940 909796 458496 / 161 > 4186 [i]