Best Known (36, 79, s)-Nets in Base 81
(36, 79, 730)-Net over F81 — Constructive and digital
Digital (36, 79, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
(36, 79, 824)-Net over F81 — Digital
Digital (36, 79, 824)-net over F81, using
(36, 79, 1330631)-Net in Base 81 — Upper bound on s
There is no (36, 79, 1330632)-net in base 81, because
- 1 times m-reduction [i] would yield (36, 78, 1330632)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 72750 065218 501995 855882 715204 460127 695757 553653 579529 497911 843915 233707 215171 622152 052103 132756 447537 384067 466130 685484 365072 517929 521251 192312 133761 > 8178 [i]