Best Known (14, ∞, s)-Nets in Base 8
(14, ∞, 65)-Net over F8 — Constructive and digital
Digital (14, m, 65)-net over F8 for arbitrarily large m, 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
(14, ∞, 115)-Net in Base 8 — Upper bound on s
There is no (14, m, 116)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (14, 105, 116)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8105, 116, S8, 91), but
- the linear programming bound shows that M ≥ 67 590695 303585 232363 449610 385167 125134 814310 899640 912361 983716 500606 168825 384014 701443 407135 513537 150976 / 996 991281 > 8105 [i]
- extracting embedded orthogonal array [i] would yield OA(8105, 116, S8, 91), but