Best Known (19, 19+28, s)-Nets in Base 81
(19, 19+28, 370)-Net over F81 — Constructive and digital
Digital (19, 47, 370)-net over F81, using
- t-expansion [i] based on digital (16, 47, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(19, 19+28, 371)-Net over F81 — Digital
Digital (19, 47, 371)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8147, 371, F81, 3, 28) (dual of [(371, 3), 1066, 29]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8144, 370, F81, 3, 28) (dual of [(370, 3), 1066, 29]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,1081P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8144, 370, F81, 3, 28) (dual of [(370, 3), 1066, 29]-NRT-code), using
(19, 19+28, 192934)-Net in Base 81 — Upper bound on s
There is no (19, 47, 192935)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 499822 827544 521112 182046 841307 232425 974206 825417 337089 879222 046560 012401 150773 443916 439201 > 8147 [i]