Best Known (78−65, 78, s)-Nets in Base 7
(78−65, 78, 21)-Net over F7 — Constructive and digital
Digital (13, 78, 21)-net over F7, using
- net from sequence [i] based on digital (13, 20)-sequence over F7, using
(78−65, 78, 48)-Net over F7 — Digital
Digital (13, 78, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
(78−65, 78, 124)-Net in Base 7 — Upper bound on s
There is no (13, 78, 125)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(778, 125, S7, 65), but
- the linear programming bound shows that M ≥ 4 472575 584895 455834 728361 845131 995948 772540 903760 570321 514418 000001 942510 894056 346118 952260 645968 920089 634920 162917 338769 306328 047062 280550 485641 / 4 909765 505447 533753 927911 208428 299748 378631 784815 695498 270105 474102 756215 514960 > 778 [i]