Best Known (56−31, 56, s)-Nets in Base 81
(56−31, 56, 370)-Net over F81 — Constructive and digital
Digital (25, 56, 370)-net over F81, using
- t-expansion [i] based on digital (16, 56, 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
(56−31, 56, 565)-Net over F81 — Digital
Digital (25, 56, 565)-net over F81, using
(56−31, 56, 798824)-Net in Base 81 — Upper bound on s
There is no (25, 56, 798825)-net in base 81, because
- 1 times m-reduction [i] would yield (25, 55, 798825)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 926 154686 324784 623852 401556 575233 386374 968180 612663 456155 782560 651705 606994 950461 211220 463352 194053 790001 > 8155 [i]