Best Known (78−66, 78, s)-Nets in Base 81
(78−66, 78, 172)-Net over F81 — Constructive and digital
Digital (12, 78, 172)-net over F81, using
- t-expansion [i] based on digital (7, 78, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(78−66, 78, 298)-Net over F81 — Digital
Digital (12, 78, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
(78−66, 78, 5319)-Net in Base 81 — Upper bound on s
There is no (12, 78, 5320)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 72859 749616 244524 458897 581426 098514 173984 459858 090745 337265 010389 735291 416339 068264 894496 295597 362409 675615 984882 472881 724413 671407 235963 808227 036801 > 8178 [i]