MinT - Best Known (137−122, 137, s)-Nets in Base 3

Best Known (137−122, 137, s)-Nets in Base 3

(137−122, 137, 28)-Net over F₃ — Constructive and digital

Digital (15, 137, 28)-net over F₃, using

net from sequence [i] based on digital (15, 27)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(137−122, 137, 40)-Net in Base 3 — Upper bound on s

There is no (15, 137, 41)-net in base 3, because

20 times m-reduction [i] would yield (15, 117, 41)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁷, 41, S₃, 3, 102), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 8008 897756 408761 320483 431092 011943 448679 786438 779805 548281 / 103 > 3¹¹⁷ [i]