Best Known (56−29, 56, s)-Nets in Base 81
(56−29, 56, 370)-Net over F81 — Constructive and digital
Digital (27, 56, 370)-net over F81, using
- t-expansion [i] based on digital (16, 56, 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
(56−29, 56, 1042)-Net over F81 — Digital
Digital (27, 56, 1042)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8156, 1042, F81, 29) (dual of [1042, 986, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8156, 1312, F81, 29) (dual of [1312, 1256, 30]-code), using
(56−29, 56, 2376765)-Net in Base 81 — Upper bound on s
There is no (27, 56, 2376766)-net in base 81, because
- 1 times m-reduction [i] would yield (27, 55, 2376766)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 926 143979 964732 993115 730005 416024 671902 711601 270706 249984 998745 156283 651039 122942 262237 123083 260521 632321 > 8155 [i]