Best Known (31, 31+36, s)-Nets in Base 8
(31, 31+36, 70)-Net over F8 — Constructive and digital
Digital (31, 67, 70)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- digital (9, 45, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- digital (4, 22, 25)-net over F8, using
(31, 31+36, 98)-Net over F8 — Digital
Digital (31, 67, 98)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(867, 98, F8, 3, 36) (dual of [(98, 3), 227, 37]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(864, 97, F8, 3, 36) (dual of [(97, 3), 227, 37]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,254P) [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(864, 97, F8, 3, 36) (dual of [(97, 3), 227, 37]-NRT-code), using
(31, 31+36, 2469)-Net in Base 8 — Upper bound on s
There is no (31, 67, 2470)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 227615 475775 369642 314218 235064 079688 471866 208006 485175 485900 > 867 [i]