Best Known (57−41, 57, s)-Nets in Base 81
(57−41, 57, 370)-Net over F81 — Constructive and digital
Digital (16, 57, 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
(57−41, 57, 22897)-Net in Base 81 — Upper bound on s
There is no (16, 57, 22898)-net in base 81, because
- 1 times m-reduction [i] would yield (16, 56, 22898)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 75045 301247 946467 766298 790782 176849 121189 821417 509335 069650 823450 448943 771195 650231 459212 046778 795708 252801 > 8156 [i]