Best Known (77−59, 77, s)-Nets in Base 5
(77−59, 77, 43)-Net over F5 — Constructive and digital
Digital (18, 77, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(77−59, 77, 116)-Net in Base 5 — Upper bound on s
There is no (18, 77, 117)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(577, 117, S5, 59), but
- the linear programming bound shows that M ≥ 2631 815329 200345 605993 124388 094335 432096 948680 855672 854372 873104 011887 335218 489170 074462 890625 / 3854 906045 660270 408433 198812 317485 186417 > 577 [i]