Best Known (32, 32+43, s)-Nets in Base 81
(32, 32+43, 370)-Net over F81 — Constructive and digital
Digital (32, 75, 370)-net over F81, using
- t-expansion [i] based on digital (16, 75, 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
(32, 32+43, 552)-Net over F81 — Digital
Digital (32, 75, 552)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8175, 552, F81, 2, 43) (dual of [(552, 2), 1029, 44]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8173, 551, F81, 2, 43) (dual of [(551, 2), 1029, 44]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,1058P) [i] based on function field F/F81 with g(F) = 30 and N(F) ≥ 551, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8173, 551, F81, 2, 43) (dual of [(551, 2), 1029, 44]-NRT-code), using
(32, 32+43, 576145)-Net in Base 81 — Upper bound on s
There is no (32, 75, 576146)-net in base 81, because
- 1 times m-reduction [i] would yield (32, 74, 576146)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 1690 019972 817973 784850 912883 368429 252000 396843 075888 795783 001698 479071 491047 233361 586804 572955 613126 685475 148844 636113 113038 825933 292308 149281 > 8174 [i]