Best Known (10, 10+44, s)-Nets in Base 7
(10, 10+44, 18)-Net over F7 — Constructive and digital
Digital (10, 54, 18)-net over F7, using
- net from sequence [i] based on digital (10, 17)-sequence over F7, using
(10, 10+44, 38)-Net over F7 — Digital
Digital (10, 54, 38)-net over F7, using
- t-expansion [i] based on digital (9, 54, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(10, 10+44, 141)-Net in Base 7 — Upper bound on s
There is no (10, 54, 142)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(754, 142, S7, 44), but
- the linear programming bound shows that M ≥ 1043 633160 134904 366249 151919 256318 081712 624562 284025 669961 563684 026338 856714 916938 626422 826308 470706 889157 138219 255341 876015 016962 / 236745 879505 932664 290074 278944 401018 052932 471641 337788 781359 657300 277485 159205 748187 > 754 [i]