Best Known (16, 16+49, s)-Nets in Base 81
(16, 16+49, 370)-Net over F81 — Constructive and digital
Digital (16, 65, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
(16, 16+49, 15039)-Net in Base 81 — Upper bound on s
There is no (16, 65, 15040)-net in base 81, because
- 1 times m-reduction [i] would yield (16, 64, 15040)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 139 179506 191468 308729 399785 431847 999771 180277 769692 670899 691754 674320 344279 070485 247056 686508 424096 884287 714609 703362 764801 > 8164 [i]