MinT - Best Known (78, 78+32, s)-Nets in Base 3

Best Known (78, 78+32, s)-Nets in Base 3

(78, 78+32, 192)-Net over F₃ — Constructive and digital

Digital (78, 110, 192)-net over F₃, using

1 times m-reduction [i] based on 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+32, 302)-Net over F₃ — Digital

Digital (78, 110, 302)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+32, 6466)-Net in Base 3 — Upper bound on s

There is no (78, 110, 6467)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30459 595124 813300 427106 039429 124095 011034 858309 278945 > 3¹¹⁰ [i]