Best Known (82−46, 82, s)-Nets in Base 81
(82−46, 82, 730)-Net over F81 — Constructive and digital
Digital (36, 82, 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
(82−46, 82, 750799)-Net in Base 81 — Upper bound on s
There is no (36, 82, 750800)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 131724 230295 066668 457097 379717 689166 150039 686792 033815 970730 496190 548127 396821 641146 818508 403977 949325 368746 954597 269096 824227 215907 077205 851771 165952 352001 > 8182 [i]