Best Known (22, 56, s)-Nets in Base 81
(22, 56, 370)-Net over F81 — Constructive and digital
Digital (22, 56, 370)-net over F81, using
- t-expansion [i] based on digital (16, 56, 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
(22, 56, 372)-Net over F81 — Digital
Digital (22, 56, 372)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8156, 372, F81, 4, 34) (dual of [(372, 4), 1432, 35]-NRT-code), using
- construction X applied to AG(4;F,1441P) ⊂ AG(4;F,1448P) [i] based on
- linear OOA(8150, 369, F81, 4, 34) (dual of [(369, 4), 1426, 35]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1441P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- linear OOA(8143, 369, F81, 4, 27) (dual of [(369, 4), 1433, 28]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1448P) [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370 (see above)
- linear OOA(816, 3, F81, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(816, 81, F81, 4, 6) (dual of [(81, 4), 318, 7]-NRT-code), using
- Reed–Solomon NRT-code RS(4;318,81) [i]
- discarding factors / shortening the dual code based on linear OOA(816, 81, F81, 4, 6) (dual of [(81, 4), 318, 7]-NRT-code), using
- construction X applied to AG(4;F,1441P) ⊂ AG(4;F,1448P) [i] based on
(22, 56, 173623)-Net in Base 81 — Upper bound on s
There is no (22, 56, 173624)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 75019 876993 830464 329557 545662 287069 236368 900793 683870 118435 087306 809281 802993 329946 034348 580859 047634 528641 > 8156 [i]