Best Known (55−39, 55, s)-Nets in Base 81
(55−39, 55, 370)-Net over F81 — Constructive and digital
Digital (16, 55, 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
(55−39, 55, 26308)-Net in Base 81 — Upper bound on s
There is no (16, 55, 26309)-net in base 81, because
- 1 times m-reduction [i] would yield (16, 54, 26309)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11 441794 948196 186194 568093 861577 493057 849025 585810 487689 638417 108320 552564 787084 059352 616279 258803 797681 > 8154 [i]