Best Known (55−42, 55, s)-Nets in Base 7
(55−42, 55, 21)-Net over F7 — Constructive and digital
Digital (13, 55, 21)-net over F7, using
- net from sequence [i] based on digital (13, 20)-sequence over F7, using
(55−42, 55, 48)-Net over F7 — Digital
Digital (13, 55, 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
(55−42, 55, 219)-Net in Base 7 — Upper bound on s
There is no (13, 55, 220)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(755, 220, S7, 42), but
- the linear programming bound shows that M ≥ 31 803577 569886 506919 445362 102828 212262 626356 674302 033878 806744 612664 857650 795288 630002 213070 327267 327360 / 1045 810749 559495 442936 757538 395832 250252 412586 401271 063043 > 755 [i]