Best Known (97−53, 97, s)-Nets in Base 16
(97−53, 97, 225)-Net over F16 — Constructive and digital
Digital (44, 97, 225)-net over F16, using
- t-expansion [i] based on digital (40, 97, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
(97−53, 97, 227)-Net over F16 — Digital
Digital (44, 97, 227)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1697, 227, F16, 2, 53) (dual of [(227, 2), 357, 54]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1697, 228, F16, 2, 53) (dual of [(228, 2), 359, 54]-NRT-code), using
- construction X applied to AG(2;F,394P) ⊂ AG(2;F,399P) [i] based on
- linear OOA(1693, 224, F16, 2, 53) (dual of [(224, 2), 355, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,394P) [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- linear OOA(1688, 224, F16, 2, 48) (dual of [(224, 2), 360, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,399P) [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225 (see above)
- linear OOA(164, 4, F16, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(164, 16, F16, 2, 4) (dual of [(16, 2), 28, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(2;28,16) [i]
- discarding factors / shortening the dual code based on linear OOA(164, 16, F16, 2, 4) (dual of [(16, 2), 28, 5]-NRT-code), using
- construction X applied to AG(2;F,394P) ⊂ AG(2;F,399P) [i] based on
- discarding factors / shortening the dual code based on linear OOA(1697, 228, F16, 2, 53) (dual of [(228, 2), 359, 54]-NRT-code), using
(97−53, 97, 19627)-Net in Base 16 — Upper bound on s
There is no (44, 97, 19628)-net in base 16, because
- 1 times m-reduction [i] would yield (44, 96, 19628)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 39 419827 551480 698921 016279 730582 726815 407262 953630 991280 716016 102559 968473 867142 312593 685831 907731 351179 917841 828046 > 1696 [i]