Best Known (3, 3+24, s)-Nets in Base 81
(3, 3+24, 116)-Net over F81 — Constructive and digital
Digital (3, 27, 116)-net over F81, using
- t-expansion [i] based on digital (2, 27, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
(3, 3+24, 136)-Net over F81 — Digital
Digital (3, 27, 136)-net over F81, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
(3, 3+24, 1295)-Net in Base 81 — Upper bound on s
There is no (3, 27, 1296)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3393 537573 548097 724528 865718 774190 165428 611122 498561 > 8127 [i]