Best Known (7, 7+81, s)-Nets in Base 16
(7, 7+81, 65)-Net over F16 — Constructive and digital
Digital (7, 88, 65)-net over F16, using
- t-expansion [i] based on digital (6, 88, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(7, 7+81, 232)-Net in Base 16 — Upper bound on s
There is no (7, 88, 233)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1688, 233, S16, 81), but
- the linear programming bound shows that M ≥ 2 303123 759933 066507 612359 910569 768348 030841 408027 733303 183433 401580 546746 955969 369266 085270 345088 485569 123058 373417 690186 093612 652008 235567 924731 097507 908838 373283 968056 001554 284544 / 242 433026 420625 726897 155194 952679 161169 829016 076892 856653 367319 641627 088539 > 1688 [i]