Best Known (30, 30+32, s)-Nets in Base 81
(30, 30+32, 370)-Net over F81 — Constructive and digital
Digital (30, 62, 370)-net over F81, using
- t-expansion [i] based on digital (16, 62, 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
(30, 30+32, 1130)-Net over F81 — Digital
Digital (30, 62, 1130)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8162, 1130, F81, 32) (dual of [1130, 1068, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(8162, 1312, F81, 32) (dual of [1312, 1250, 33]-code), using
(30, 30+32, 2112645)-Net in Base 81 — Upper bound on s
There is no (30, 62, 2112646)-net in base 81, because
- 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]