Best Known (73−41, 73, s)-Nets in Base 81
(73−41, 73, 370)-Net over F81 — Constructive and digital
Digital (32, 73, 370)-net over F81, using
- t-expansion [i] based on digital (16, 73, 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
(73−41, 73, 620)-Net over F81 — Digital
Digital (32, 73, 620)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8173, 620, F81, 41) (dual of [620, 547, 42]-code), using
- 114 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 13 times 0, 1, 37 times 0, 1, 58 times 0) [i] based on linear OA(8167, 500, F81, 41) (dual of [500, 433, 42]-code), using
- extended algebraic-geometric code AGe(F,458P) [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
- 114 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 13 times 0, 1, 37 times 0, 1, 58 times 0) [i] based on linear OA(8167, 500, F81, 41) (dual of [500, 433, 42]-code), using
(73−41, 73, 770471)-Net in Base 81 — Upper bound on s
There is no (32, 73, 770472)-net in base 81, because
- 1 times m-reduction [i] would yield (32, 72, 770472)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 257585 995835 036581 884483 404212 024119 639452 204959 894646 095744 090844 947369 175968 089293 643219 724513 869777 805855 143739 315701 782918 445700 723201 > 8172 [i]