Best Known (37−21, 37, s)-Nets in Base 81
(37−21, 37, 370)-Net over F81 — Constructive and digital
Digital (16, 37, 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
(37−21, 37, 401)-Net over F81 — Digital
Digital (16, 37, 401)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8137, 401, F81, 21) (dual of [401, 364, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 410, F81, 21) (dual of [410, 373, 22]-code), using
(37−21, 37, 420172)-Net in Base 81 — Upper bound on s
There is no (16, 37, 420173)-net in base 81, because
- 1 times m-reduction [i] would yield (16, 36, 420173)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 507 535069 510431 276110 891103 216064 867079 116423 918669 491602 935550 826401 > 8136 [i]