Best Known (31, 65, s)-Nets in Base 81
(31, 65, 370)-Net over F81 — Constructive and digital
Digital (31, 65, 370)-net over F81, using
- t-expansion [i] based on digital (16, 65, 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
(31, 65, 1034)-Net over F81 — Digital
Digital (31, 65, 1034)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8165, 1034, F81, 34) (dual of [1034, 969, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8165, 1312, F81, 34) (dual of [1312, 1247, 35]-code), using
(31, 65, 1778286)-Net in Base 81 — Upper bound on s
There is no (31, 65, 1778287)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 11259 701350 698021 631631 473927 086280 662471 652750 316284 078404 496799 316378 414763 102839 968972 739636 423968 320092 404262 775603 801521 > 8165 [i]