Best Known (31, 31+36, s)-Nets in Base 81
(31, 31+36, 370)-Net over F81 — Constructive and digital
Digital (31, 67, 370)-net over F81, using
- t-expansion [i] based on digital (16, 67, 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
(31, 31+36, 800)-Net over F81 — Digital
Digital (31, 67, 800)-net over F81, using
(31, 31+36, 1199063)-Net in Base 81 — Upper bound on s
There is no (31, 67, 1199064)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 73 875117 225893 343501 009339 916028 217899 170739 110183 803424 632536 599822 117929 050709 396697 220017 797988 474921 862617 976197 841666 108161 > 8167 [i]