Best Known (239−116, 239, s)-Nets in Base 3
(239−116, 239, 78)-Net over F3 — Constructive and digital
Digital (123, 239, 78)-net over F3, using
- t-expansion [i] based on digital (121, 239, 78)-net over F3, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
(239−116, 239, 127)-Net over F3 — Digital
Digital (123, 239, 127)-net over F3, using
(239−116, 239, 981)-Net in Base 3 — Upper bound on s
There is no (123, 239, 982)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 079318 302707 611328 892988 779056 570075 965891 118690 605169 007559 453238 051222 640522 135354 264127 081636 973529 151799 058365 > 3239 [i]