Best Known (29, 29+68, s)-Nets in Base 5
(29, 29+68, 51)-Net over F5 — Constructive and digital
Digital (29, 97, 51)-net over F5, using
- t-expansion [i] based on digital (22, 97, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(29, 29+68, 56)-Net over F5 — Digital
Digital (29, 97, 56)-net over F5, using
- net from sequence [i] based on digital (29, 55)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 29 and N(F) ≥ 56, using
(29, 29+68, 299)-Net in Base 5 — Upper bound on s
There is no (29, 97, 300)-net in base 5, because
- 3 times m-reduction [i] would yield (29, 94, 300)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(594, 300, S5, 65), but
- the linear programming bound shows that M ≥ 10516 954940 091904 344602 480640 722591 906961 543685 679547 040672 489731 680698 471397 118291 128675 167720 811692 906879 012474 923687 312150 789429 563965 858002 578244 480285 096784 655252 122320 234775 543212 890625 / 17178 139436 360288 168843 954862 452950 441117 585418 463584 208857 078043 700354 226203 170629 797935 345060 016501 538131 593077 429209 923377 > 594 [i]
- extracting embedded orthogonal array [i] would yield OA(594, 300, S5, 65), but