Best Known (32, 32+35, s)-Nets in Base 81
(32, 32+35, 370)-Net over F81 — Constructive and digital
Digital (32, 67, 370)-net over F81, using
- t-expansion [i] based on digital (16, 67, 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
(32, 32+35, 1065)-Net over F81 — Digital
Digital (32, 67, 1065)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8167, 1065, F81, 35) (dual of [1065, 998, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8167, 1312, F81, 35) (dual of [1312, 1245, 36]-code), using
(32, 32+35, 2302852)-Net in Base 81 — Upper bound on s
There is no (32, 67, 2302853)-net in base 81, because
- 1 times m-reduction [i] would yield (32, 66, 2302853)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 912038 701853 090385 001974 527057 126456 415615 127704 131582 562471 993937 129918 122076 904300 467590 852763 569829 623445 737480 132203 342481 > 8166 [i]