Best Known (90−65, 90, s)-Nets in Base 4
(90−65, 90, 34)-Net over F4 — Constructive and digital
Digital (25, 90, 34)-net over F4, using
- t-expansion [i] based on digital (21, 90, 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
(90−65, 90, 35)-Net in Base 4 — Constructive
(25, 90, 35)-net in base 4, using
- t-expansion [i] based on (24, 90, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-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 2 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]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
(90−65, 90, 51)-Net over F4 — Digital
Digital (25, 90, 51)-net over F4, using
- net from sequence [i] based on digital (25, 50)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 25 and N(F) ≥ 51, using
(90−65, 90, 112)-Net in Base 4 — Upper bound on s
There is no (25, 90, 113)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(490, 113, S4, 65), but
- the linear programming bound shows that M ≥ 3 505790 269169 705234 956014 427184 836399 026829 839938 462474 722585 241140 068352 / 1 861467 044653 198125 > 490 [i]