Best Known (67−41, 67, s)-Nets in Base 81
(67−41, 67, 370)-Net over F81 — Constructive and digital
Digital (26, 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
(67−41, 67, 500)-Net over F81 — Digital
Digital (26, 67, 500)-net over F81, using
- net from sequence [i] based on digital (26, 499)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
(67−41, 67, 206156)-Net in Base 81 — Upper bound on s
There is no (26, 67, 206157)-net in base 81, because
- 1 times m-reduction [i] would yield (26, 66, 206157)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 912110 835192 527833 933382 528945 536525 414184 684282 503794 683936 049567 563600 325778 618999 113163 460087 634728 325478 884143 276767 419201 > 8166 [i]