Best Known (64−42, 64, s)-Nets in Base 81
(64−42, 64, 370)-Net over F81 — Constructive and digital
Digital (22, 64, 370)-net over F81, using
- t-expansion [i] based on digital (16, 64, 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
(64−42, 64, 71068)-Net in Base 81 — Upper bound on s
There is no (22, 64, 71069)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 139 042302 498842 579282 853356 344064 324581 779481 032257 060139 347465 864261 205348 635695 733285 016355 445074 813472 382861 478750 755921 > 8164 [i]