Best Known (28, 66, s)-Nets in Base 81
(28, 66, 370)-Net over F81 — Constructive and digital
Digital (28, 66, 370)-net over F81, using
- t-expansion [i] based on digital (16, 66, 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
(28, 66, 501)-Net over F81 — Digital
Digital (28, 66, 501)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8166, 501, F81, 2, 38) (dual of [(501, 2), 936, 39]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8164, 500, F81, 2, 38) (dual of [(500, 2), 936, 39]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,961P) [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8164, 500, F81, 2, 38) (dual of [(500, 2), 936, 39]-NRT-code), using
(28, 66, 422270)-Net in Base 81 — Upper bound on s
There is no (28, 66, 422271)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 912072 825594 187451 253104 653367 688246 745359 115317 603655 227592 394602 705009 488754 428931 136088 075008 123676 070612 949091 660351 906321 > 8166 [i]