MinT - Best Known (151, 151+49, s)-Nets in Base 3

Best Known (151, 151+49, s)-Nets in Base 3

(151, 151+49, 400)-Net over F₃ — Constructive and digital

Digital (151, 200, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 50, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(151, 151+49, 921)-Net over F₃ — Digital

Digital (151, 200, 921)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+49, 44282)-Net in Base 3 — Upper bound on s

There is no (151, 200, 44283)-net in base 3, because

1 times m-reduction [i] would yield (151, 199, 44283)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88558 787342 491193 518778 027279 190230 715701 655260 295517 206122 840006 839135 355012 462166 085245 925713 > 3¹⁹⁹ [i]