Best Known (6, 78, s)-Nets in Base 16
(6, 78, 65)-Net over F16 — Constructive and digital
Digital (6, 78, 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
(6, 78, 212)-Net in Base 16 — Upper bound on s
There is no (6, 78, 213)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1678, 213, S16, 72), but
- the linear programming bound shows that M ≥ 168 318081 526394 556736 598990 893763 195201 223162 752431 371588 827269 540156 318632 738471 715543 975957 870504 525709 620174 110510 036117 592416 392278 458492 594786 664448 / 19971 672319 322313 553712 770443 596511 113891 451429 162319 655841 > 1678 [i]