Best Known (18, 18+49, s)-Nets in Base 81
(18, 18+49, 370)-Net over F81 — Constructive and digital
Digital (18, 67, 370)-net over F81, using
- t-expansion [i] based on digital (16, 67, 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
(18, 18+49, 21695)-Net in Base 81 — Upper bound on s
There is no (18, 67, 21696)-net in base 81, because
- 1 times m-reduction [i] would yield (18, 66, 21696)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 912500 035603 534733 002162 038116 610606 585041 367847 039896 857969 424054 967005 558437 262483 223886 161293 244075 529700 019064 200247 582721 > 8166 [i]