Best Known (68−51, 68, s)-Nets in Base 5
(68−51, 68, 42)-Net over F5 — Constructive and digital
Digital (17, 68, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(68−51, 68, 140)-Net in Base 5 — Upper bound on s
There is no (17, 68, 141)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(568, 141, S5, 51), but
- the linear programming bound shows that M ≥ 819563 040333 764860 431491 254131 972234 907785 149666 341437 906639 890370 299586 341735 680893 493666 840815 169039 411339 854235 312063 276058 287999 522688 158259 970588 459215 023601 895377 816128 011091 556800 224811 963285 460929 055736 020081 981662 775421 506810 405816 202680 373550 037984 387017 786502 838134 765625 / 2 361679 377224 266490 557562 861346 683547 335016 861722 504804 330694 911263 181294 697046 447488 417854 663289 149334 352277 049917 339413 751666 213290 236811 034133 310896 287939 078597 945247 742045 367171 823259 008208 494753 616393 569184 028532 725177 300481 985141 > 568 [i]