Best Known (83−65, 83, s)-Nets in Base 27
(83−65, 83, 108)-Net over F27 — Constructive and digital
Digital (18, 83, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
(83−65, 83, 148)-Net over F27 — Digital
Digital (18, 83, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
(83−65, 83, 2272)-Net in Base 27 — Upper bound on s
There is no (18, 83, 2273)-net in base 27, because
- 1 times m-reduction [i] would yield (18, 82, 2273)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2354 569838 882087 948551 825877 896771 231274 253105 538997 659672 608288 496647 164074 226299 081516 505399 926455 125531 054365 723521 > 2782 [i]