Best Known (36, 75, s)-Nets in Base 81
(36, 75, 730)-Net over F81 — Constructive and digital
Digital (36, 75, 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
(36, 75, 1185)-Net over F81 — Digital
Digital (36, 75, 1185)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8175, 1185, F81, 39) (dual of [1185, 1110, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(8175, 1312, F81, 39) (dual of [1312, 1237, 40]-code), using
(36, 75, 2686401)-Net in Base 81 — Upper bound on s
There is no (36, 75, 2686402)-net in base 81, because
- 1 times m-reduction [i] would yield (36, 74, 2686402)-net in base 81, but
- 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]