Best Known (64−51, 64, s)-Nets in Base 7
(64−51, 64, 21)-Net over F7 — Constructive and digital
Digital (13, 64, 21)-net over F7, using
- net from sequence [i] based on digital (13, 20)-sequence over F7, using
(64−51, 64, 48)-Net over F7 — Digital
Digital (13, 64, 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
(64−51, 64, 190)-Net in Base 7 — Upper bound on s
There is no (13, 64, 191)-net in base 7, because
- 1 times m-reduction [i] would yield (13, 63, 191)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(763, 191, S7, 50), but
- the linear programming bound shows that M ≥ 1546 656467 224859 842887 981514 622928 628845 010308 476857 250636 511791 494639 882610 915125 941329 017991 447474 997780 955993 395167 734335 889066 511289 351740 816250 / 8321 117215 862883 682551 397462 523193 233196 670318 520045 231419 117539 569361 618123 026216 299968 870299 > 763 [i]
- extracting embedded orthogonal array [i] would yield OA(763, 191, S7, 50), but