Best Known (63−33, 63, s)-Nets in Base 81
(63−33, 63, 370)-Net over F81 — Constructive and digital
Digital (30, 63, 370)-net over F81, using
- t-expansion [i] based on digital (16, 63, 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
(63−33, 63, 1004)-Net over F81 — Digital
Digital (30, 63, 1004)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8163, 1004, F81, 33) (dual of [1004, 941, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8163, 1312, F81, 33) (dual of [1312, 1249, 34]-code), using
(63−33, 63, 2112645)-Net in Base 81 — Upper bound on s
There is no (30, 63, 2112646)-net in base 81, because
- 1 times m-reduction [i] would yield (30, 62, 2112646)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 21187 183686 238568 046472 220778 302428 043963 742767 191298 914720 198961 219832 437471 924624 758011 032473 399352 281742 425145 914881 > 8162 [i]