Best Known (88−67, 88, s)-Nets in Base 5
(88−67, 88, 43)-Net over F5 — Constructive and digital
Digital (21, 88, 43)-net over F5, using
- t-expansion [i] based on digital (18, 88, 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]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(88−67, 88, 50)-Net over F5 — Digital
Digital (21, 88, 50)-net over F5, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(88−67, 88, 133)-Net in Base 5 — Upper bound on s
There is no (21, 88, 134)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(588, 134, S5, 67), but
- the linear programming bound shows that M ≥ 4831 235646 169965 390833 091690 607745 568309 913723 515187 884775 076145 767076 592663 254175 352705 033219 535835 087299 346923 828125 / 134 629040 721585 738105 452669 020425 617638 636857 171077 234688 > 588 [i]