Best Known (68−47, 68, s)-Nets in Base 81
(68−47, 68, 370)-Net over F81 — Constructive and digital
Digital (21, 68, 370)-net over F81, using
- t-expansion [i] based on digital (16, 68, 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
(68−47, 68, 42731)-Net in Base 81 — Upper bound on s
There is no (21, 68, 42732)-net in base 81, because
- 1 times m-reduction [i] would yield (21, 67, 42732)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 73 881777 812044 708321 027334 142320 420653 934620 173589 683654 092450 320218 828458 648138 265287 663654 532517 064242 742879 387678 968043 132481 > 8167 [i]