Best Known (72−58, 72, s)-Nets in Base 8
(72−58, 72, 65)-Net over F8 — Constructive and digital
Digital (14, 72, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
(72−58, 72, 267)-Net in Base 8 — Upper bound on s
There is no (14, 72, 268)-net in base 8, because
- 7 times m-reduction [i] would yield (14, 65, 268)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(865, 268, S8, 51), but
- the linear programming bound shows that M ≥ 30459 303481 650707 900837 373363 759359 419150 640173 960998 299207 839857 962602 380988 612501 058636 935514 792000 944994 950889 307502 637135 953920 000000 / 565283 209718 686154 793936 730925 378972 076311 663982 211625 079920 971613 273614 112183 > 865 [i]
- extracting embedded orthogonal array [i] would yield OA(865, 268, S8, 51), but