Best Known (68, 68+37, s)-Nets in Base 27
(68, 68+37, 546)-Net over F27 — Constructive and digital
Digital (68, 105, 546)-net over F27, using
- net defined by OOA [i] based on linear OOA(27105, 546, F27, 37, 37) (dual of [(546, 37), 20097, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(27105, 9829, F27, 37) (dual of [9829, 9724, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(27105, 9841, F27, 37) (dual of [9841, 9736, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(27105, 9829, F27, 37) (dual of [9829, 9724, 38]-code), using
(68, 68+37, 730)-Net in Base 27 — Constructive
(68, 105, 730)-net in base 27, using
- t-expansion [i] based on (63, 105, 730)-net in base 27, using
- 3 times m-reduction [i] based on (63, 108, 730)-net in base 27, using
- base change [i] based on digital (36, 81, 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
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- base change [i] based on digital (36, 81, 730)-net over F81, using
- 3 times m-reduction [i] based on (63, 108, 730)-net in base 27, using
(68, 68+37, 9565)-Net over F27 — Digital
Digital (68, 105, 9565)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27105, 9565, F27, 37) (dual of [9565, 9460, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(27105, 9841, F27, 37) (dual of [9841, 9736, 38]-code), using
(68, 68+37, large)-Net in Base 27 — Upper bound on s
There is no (68, 105, large)-net in base 27, because
- 35 times m-reduction [i] would yield (68, 70, large)-net in base 27, but