Best Known (68−50, 68, s)-Nets in Base 5
(68−50, 68, 43)-Net over F5 — Constructive and digital
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]
(68−50, 68, 172)-Net in Base 5 — Upper bound on s
There is no (18, 68, 173)-net in base 5, because
- 2 times m-reduction [i] would yield (18, 66, 173)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(566, 173, S5, 48), but
- the linear programming bound shows that M ≥ 674903 106323 478763 038018 560328 405964 641412 538237 106534 354217 727811 147236 947337 773516 736317 010284 549564 365652 596364 952842 122875 154018 402099 609375 / 48 652639 875561 652308 337532 364210 952712 444109 849771 786000 198245 773574 375778 397008 862648 659456 252292 > 566 [i]
- extracting embedded orthogonal array [i] would yield OA(566, 173, S5, 48), but