Best Known (91−70, 91, s)-Nets in Base 5
(91−70, 91, 43)-Net over F5 — Constructive and digital
Digital (21, 91, 43)-net over F5, using
- t-expansion [i] based on digital (18, 91, 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
(91−70, 91, 50)-Net over F5 — Digital
Digital (21, 91, 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
(91−70, 91, 121)-Net in Base 5 — Upper bound on s
There is no (21, 91, 122)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(591, 122, S5, 70), but
- the linear programming bound shows that M ≥ 641436 961643 670486 170401 619030 430750 031978 706150 216640 313743 710066 773928 701877 593994 140625 / 118 037188 358392 601580 033024 > 591 [i]