Best Known (74−38, 74, s)-Nets in Base 81
(74−38, 74, 730)-Net over F81 — Constructive and digital
Digital (36, 74, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
(74−38, 74, 1307)-Net over F81 — Digital
Digital (36, 74, 1307)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8174, 1307, F81, 38) (dual of [1307, 1233, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(8174, 1313, F81, 38) (dual of [1313, 1239, 39]-code), using
(74−38, 74, 2686401)-Net in Base 81 — Upper bound on s
There is no (36, 74, 2686402)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 1690 022730 894282 705574 525293 977717 052409 078999 454310 867993 563330 805702 118647 883071 324483 625679 373911 729066 798324 632740 659622 769618 298115 926241 > 8174 [i]