Best Known (7, 7+83, s)-Nets in Base 16
(7, 7+83, 65)-Net over F16 — Constructive and digital
Digital (7, 90, 65)-net over F16, using
- t-expansion [i] based on digital (6, 90, 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+83, 228)-Net in Base 16 — Upper bound on s
There is no (7, 90, 229)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1690, 229, S16, 83), but
- the linear programming bound shows that M ≥ 812 538869 320548 166981 783916 899363 998507 094127 753957 854160 175340 985631 046096 726772 806904 003069 714541 706567 360155 408657 577389 783566 428338 140709 281691 652538 769466 225603 832481 990049 792000 / 340 693885 016018 060919 658351 039684 171232 027797 695571 668789 618340 253666 717541 > 1690 [i]