MinT - Best Known (103, 103+44, s)-Nets in Base 3

Best Known (103, 103+44, s)-Nets in Base 3

(103, 103+44, 204)-Net over F₃ — Constructive and digital

Digital (103, 147, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 49, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(103, 103+44, 344)-Net over F₃ — Digital

Digital (103, 147, 344)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+44, 6958)-Net in Base 3 — Upper bound on s

There is no (103, 147, 6959)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13720 159212 032886 808823 062107 606213 802566 337239 310947 635436 795347 875509 > 3¹⁴⁷ [i]