Best Known (16, 34, s)-Nets in Base 81
(16, 34, 370)-Net over F81 — Constructive and digital
Digital (16, 34, 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
(16, 34, 727)-Net over F81 — Digital
Digital (16, 34, 727)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8134, 727, F81, 18) (dual of [727, 693, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8134, 1312, F81, 18) (dual of [1312, 1278, 19]-code), using
(16, 34, 840410)-Net in Base 81 — Upper bound on s
There is no (16, 34, 840411)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 77355 559265 980039 961888 099263 013281 689471 929613 356318 018142 990321 > 8134 [i]