Best Known (35−19, 35, s)-Nets in Base 81
(35−19, 35, 370)-Net over F81 — Constructive and digital
Digital (16, 35, 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
(35−19, 35, 581)-Net over F81 — Digital
Digital (16, 35, 581)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8135, 581, F81, 19) (dual of [581, 546, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8135, 656, F81, 19) (dual of [656, 621, 20]-code), using
(35−19, 35, 840410)-Net in Base 81 — Upper bound on s
There is no (16, 35, 840411)-net in base 81, because
- 1 times m-reduction [i] would yield (16, 34, 840411)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 77355 559265 980039 961888 099263 013281 689471 929613 356318 018142 990321 > 8134 [i]