Best Known (69−36, 69, s)-Nets in Base 81
(69−36, 69, 370)-Net over F81 — Constructive and digital
Digital (33, 69, 370)-net over F81, using
- t-expansion [i] based on digital (16, 69, 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
(69−36, 69, 1095)-Net over F81 — Digital
Digital (33, 69, 1095)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8169, 1095, F81, 36) (dual of [1095, 1026, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8169, 1312, F81, 36) (dual of [1312, 1243, 37]-code), using
(69−36, 69, 1953877)-Net in Base 81 — Upper bound on s
There is no (33, 69, 1953878)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 484693 980208 124333 540668 526137 300528 199026 499847 385335 236986 470460 565258 563353 569602 374630 138318 080393 572760 121897 183582 660318 179521 > 8169 [i]