Best Known (76−40, 76, s)-Nets in Base 81
(76−40, 76, 730)-Net over F81 — Constructive and digital
Digital (36, 76, 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
(76−40, 76, 1027)-Net over F81 — Digital
Digital (36, 76, 1027)-net over F81, using
(76−40, 76, 1855483)-Net in Base 81 — Upper bound on s
There is no (36, 76, 1855484)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 11 088301 833653 644995 020115 230597 863212 493625 515295 339243 891258 521561 483277 489170 795494 071977 632940 131425 893439 381192 843050 160527 320724 464724 294401 > 8176 [i]