Best Known (74−49, 74, s)-Nets in Base 81
(74−49, 74, 370)-Net over F81 — Constructive and digital
Digital (25, 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
(74−49, 74, 392)-Net over F81 — Digital
Digital (25, 74, 392)-net over F81, using
- net from sequence [i] based on digital (25, 391)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 25 and N(F) ≥ 392, using
(74−49, 74, 78195)-Net in Base 81 — Upper bound on s
There is no (25, 74, 78196)-net in base 81, because
- 1 times m-reduction [i] would yield (25, 73, 78196)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 20 866789 426588 266636 001439 504668 787759 931168 041752 376602 847219 998988 979589 976628 158743 159130 969160 448373 220128 062715 569574 802635 388842 462721 > 8173 [i]