Best Known (37−20, 37, s)-Nets in Base 81
(37−20, 37, 370)-Net over F81 — Constructive and digital
Digital (17, 37, 370)-net over F81, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(37−20, 37, 612)-Net over F81 — Digital
Digital (17, 37, 612)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8137, 612, F81, 20) (dual of [612, 575, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 656, F81, 20) (dual of [656, 619, 21]-code), using
(37−20, 37, 652045)-Net in Base 81 — Upper bound on s
There is no (17, 37, 652046)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 41110 238112 043635 085288 962325 496262 535634 825261 642851 830326 597540 804801 > 8137 [i]