Best Known (64−49, 64, s)-Nets in Base 5
(64−49, 64, 36)-Net over F5 — Constructive and digital
Digital (15, 64, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(64−49, 64, 39)-Net over F5 — Digital
Digital (15, 64, 39)-net over F5, using
- t-expansion [i] based on digital (14, 64, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(64−49, 64, 112)-Net in Base 5 — Upper bound on s
There is no (15, 64, 113)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(564, 113, S5, 49), but
- the linear programming bound shows that M ≥ 156606 210358 824936 582349 373022 311212 937060 941451 069127 521993 338668 053985 230882 148782 901484 641130 932895 340677 202256 074451 724998 652935 028076 171875 / 267 291464 691824 785899 503749 748874 718481 761014 320571 914004 118955 970335 822493 496252 091117 857604 462643 > 564 [i]