Best Known (59−47, 59, s)-Nets in Base 7
(59−47, 59, 20)-Net over F7 — Constructive and digital
Digital (12, 59, 20)-net over F7, using
- net from sequence [i] based on digital (12, 19)-sequence over F7, using
(59−47, 59, 38)-Net over F7 — Digital
Digital (12, 59, 38)-net over F7, using
- t-expansion [i] based on digital (9, 59, 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
(59−47, 59, 177)-Net in Base 7 — Upper bound on s
There is no (12, 59, 178)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(759, 178, S7, 47), but
- the linear programming bound shows that M ≥ 295036 613560 653670 440697 947380 192400 909003 620734 292487 545853 626254 349789 678638 856783 680977 093856 250794 251401 332898 643666 580118 276653 126601 / 3952 418576 558777 425638 126263 521724 491571 860969 653559 610745 682469 911768 695167 314775 418521 > 759 [i]