Best Known (18, 18+42, s)-Nets in Base 81
(18, 18+42, 370)-Net over F81 — Constructive and digital
Digital (18, 60, 370)-net over F81, using
- t-expansion [i] based on digital (16, 60, 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+42, 30766)-Net in Base 81 — Upper bound on s
There is no (18, 60, 30767)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 231285 821374 781573 705401 020876 742250 137681 738765 253957 817514 370693 089716 501609 536953 099403 948625 333784 354704 360561 > 8160 [i]