MinT - Best Known (78, 78+33, s)-Nets in Base 3

Best Known (78, 78+33, s)-Nets in Base 3

(78, 78+33, 192)-Net over F₃ — Constructive and digital

Digital (78, 111, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 37, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(78, 78+33, 282)-Net over F₃ — Digital

Digital (78, 111, 282)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+33, 6466)-Net in Base 3 — Upper bound on s

There is no (78, 111, 6467)-net in base 3, because

1 times m-reduction [i] would yield (78, 110, 6467)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30459 595124 813300 427106 039429 124095 011034 858309 278945 > 3¹¹⁰ [i]