MinT - Best Known (78, 78+28, s)-Nets in Base 3

Best Known (78, 78+28, s)-Nets in Base 3

(78, 78+28, 246)-Net over F₃ — Constructive and digital

Digital (78, 106, 246)-net over F₃, using

3¹ times duplication [i] based on digital (77, 105, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 35, 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]

(78, 78+28, 421)-Net over F₃ — Digital

Digital (78, 106, 421)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+28, 12372)-Net in Base 3 — Upper bound on s

There is no (78, 106, 12373)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 376 087639 491980 263351 301764 235494 408621 136071 630209 > 3¹⁰⁶ [i]