MinT - Best Known (79, 79+29, s)-Nets in Base 3

Best Known (79, 79+29, s)-Nets in Base 3

(79, 79+29, 246)-Net over F₃ — Constructive and digital

Digital (79, 108, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 36, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(79, 79+29, 402)-Net over F₃ — Digital

Digital (79, 108, 402)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+29, 13383)-Net in Base 3 — Upper bound on s

There is no (79, 108, 13384)-net in base 3, because

1 times m-reduction [i] would yield (79, 107, 13384)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1128 084732 462203 932872 899219 958171 784001 722093 781553 > 3¹⁰⁷ [i]