MinT - Best Known (48−31, 48, s)-Nets in Base 3

Best Known (48−31, 48, s)-Nets in Base 3

(48−31, 48, 28)-Net over F₃ — Constructive and digital

Digital (17, 48, 28)-net over F₃, using

t-expansion [i] based on digital (15, 48, 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]

(48−31, 48, 73)-Net in Base 3 — Upper bound on s

There is no (17, 48, 74)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁸, 74, S₃, 31), but
- the linear programming bound shows that MÂ â‰¥ 5 960874 730507 377196 420194 390341 917191 / 66 651128 760320 > 3⁴⁸ [i]