Best Known (19, 19+55, s)-Nets in Base 81
(19, 19+55, 370)-Net over F81 — Constructive and digital
Digital (19, 74, 370)-net over F81, using
- t-expansion [i] based on digital (16, 74, 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+55, 19724)-Net in Base 81 — Upper bound on s
There is no (19, 74, 19725)-net in base 81, because
- 1 times m-reduction [i] would yield (19, 73, 19725)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 20 884843 089875 562164 951003 154663 419967 251807 272508 042524 922846 305029 858033 757704 929351 195662 300768 763207 723062 855764 812925 955063 462339 726001 > 8173 [i]