Best Known (80−56, 80, s)-Nets in Base 4
(80−56, 80, 34)-Net over F4 — Constructive and digital
Digital (24, 80, 34)-net over F4, using
- t-expansion [i] based on digital (21, 80, 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
(80−56, 80, 35)-Net in Base 4 — Constructive
(24, 80, 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
(80−56, 80, 49)-Net over F4 — Digital
Digital (24, 80, 49)-net over F4, using
- net from sequence [i] based on digital (24, 48)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 24 and N(F) ≥ 49, using
(80−56, 80, 136)-Net in Base 4 — Upper bound on s
There is no (24, 80, 137)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(480, 137, S4, 56), but
- the linear programming bound shows that M ≥ 4 659960 221203 496853 163226 363837 259299 550270 044661 307956 982242 869378 543300 762197 724251 227847 275888 362314 153741 098349 220963 866857 421716 586496 / 2 984505 831211 110314 590234 720839 251843 308173 814966 404669 702639 349464 655855 193225 040329 041725 > 480 [i]