Best Known (19, 19+32, s)-Nets in Base 81
(19, 19+32, 370)-Net over F81 — Constructive and digital
Digital (19, 51, 370)-net over F81, using
- t-expansion [i] based on digital (16, 51, 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+32, 102970)-Net in Base 81 — Upper bound on s
There is no (19, 51, 102971)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 21 516848 906858 332698 981225 073901 866570 654977 307322 445162 233077 381513 584246 720240 448445 230579 930881 > 8151 [i]