Best Known (19, 19+58, s)-Nets in Base 81
(19, 19+58, 370)-Net over F81 — Constructive and digital
Digital (19, 77, 370)-net over F81, using
- t-expansion [i] based on digital (16, 77, 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+58, 17022)-Net in Base 81 — Upper bound on s
There is no (19, 77, 17023)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 898 954299 230861 544580 298937 823281 437512 125316 488339 897656 499689 397712 566817 687971 349438 730795 884441 243622 833706 676791 049050 904773 452822 598471 851761 > 8177 [i]