Best Known (68−47, 68, s)-Nets in Base 5
(68−47, 68, 43)-Net over F5 — Constructive and digital
Digital (21, 68, 43)-net over F5, using
- t-expansion [i] based on digital (18, 68, 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
(68−47, 68, 50)-Net over F5 — Digital
Digital (21, 68, 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
(68−47, 68, 233)-Net in Base 5 — Upper bound on s
There is no (21, 68, 234)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(568, 234, S5, 47), but
- the linear programming bound shows that M ≥ 2 159165 606935 321284 794791 064224 821708 176918 361680 776590 449296 722527 246974 173920 079920 208081 603050 231933 593750 000000 / 6 283037 652750 309196 863831 272958 587304 853780 440221 088369 548641 006293 > 568 [i]