Best Known (19, 19+52, s)-Nets in Base 81
(19, 19+52, 370)-Net over F81 — Constructive and digital
Digital (19, 71, 370)-net over F81, using
- t-expansion [i] based on digital (16, 71, 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
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(19, 19+52, 21457)-Net in Base 81 — Upper bound on s
There is no (19, 71, 21458)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3182 635350 474611 219057 481348 685028 459938 444553 274381 248116 253115 467684 067713 771310 084749 359764 464274 387678 949376 007469 663175 096387 512641 > 8171 [i]